Contoh Soal Himpunan Matematika dan Pembahasannya Kelas 7 SMP

Contoh Soal Himpunan MatematikaSetelah kalian mempelajari materi tentang himpunan matematika, ada baiknya kalian juga memperhatikan contoh soal dan pembahasan mengenai himpunan yang akan diberikan oleh rumus matematika dasar pada artikel ini. Mempelajari contoh-contoh soal akan mempermuda kalian dalam memahami materi serta cara menjawab soal-soal yang berkaitan dengan sebuah materi pelajaran matematika.

Untuk bisa menjawab soal-soal latihan mengenai himpunan, kalian sebelumnya harus mengerti terlebih dahulu mengenai diagram venn serta konsep dasar dari himpunan matematika. Jika kalian sudah merasa menguasainya, silahkan kalian simak pembahasan soal berikut ini:

Contoh Soal dan Pembahasan Himpunan Matematika Kelas 7 SMP Lengkap


Contoh Soal 1:

Dari 42 kambing yang ada di kandang milik pak Arman, 30 kambing menyukai rumput gajah, dan 28 ekor kambing menyukai rumput teki. apabila ada 4 ekor kambing yang tidak menyukai kedua rumput tersebut, berapa ekor kambing yang menyukai rumput gajah dan rumput teki?

Pembahasan:

untuk mencarinya, kita gunakan rumus himpunan berikut:

n{AΛB} = (n{A} + n{B}) - (n{S} - n{X})
n{AΛB} = (30 + 28) - (42 - 4)
n{AΛB} = 58 - 38
n{AΛB} = 20

Jadi, jumlah kambing yang menyukai kedua jenis rumput tersebut adalah 20 ekor.


Contoh Soal 2:

Siswa kelas 7 SMP Tunas Mekar adalah 45. tiap-tiap siswa memilih dua jenis pelajaran yang mereka sukai. diketahui ada 27 siswa yang menyukai pelajaran Matematika dan 26 siswa menyukai pelajaran Bahasa Inggris. Sementara siswa yang tidak menyukai kedua pelajaran tersebut ada 5 orang. Tentukanlah banyaknya siswa yang menyukai pelajaran bahasa inggris dan matematika serta gambarlah diagram venn-nya.

Pembahasan:

Kita cari terlebih dahulu jumlah siswa yang menyukai kedua pelajaran tersebut:

n{AΛB} = (n{A} + n{B}) - (n{S} - n{X})
n{AΛB} = (27 + 26) – (45 – 5)
n{AΛB} = 13

Maka dapat disimpulkan bahwa:
Siswa yang menyukai matematika saja = 27 - 13 = 14 siswa
Siswa yang menyukai bahasa inggris saja = 26 - 13 = 13 siswa

Maka gambar diagram venn-nya adalah:

Contoh Soal Himpunan Matematika dan Pembahasannya Kelas 7 SMP


Contoh Soal 3:


Di dalam sebuah ruangan terdapat 150 siswa yang baru lulus SMP. Diketahui ada 75 siswa memilih untuk masuk SMA dan 63 siswa memilih untuk masuk SMK sementara ada 32 siswa yang belum menentukan pilihannya. Lalu, berapakah banyaknya siswa yang hanya memilih untuk masuk SMA dan SMK saja?

Pembahasan:

Siswa yang memilih masuk SMA dan SMK adalah:

n{AΛB} = (n{A} + n{B}) - (n{S} - n{X})
n{AΛB} = (75 + 63) – (150 – 32)
n{AΛB} = 138 – 118
n{AΛB} = 20 siswa

Siswa yang memilih masuk SMA saja = 75 – 20 = 55 orang
Siswa yang mmeilih masuk SMK saja = 63 – 20 = 43 orang


Contoh Soal 4:

Dari 40 orang bayi, diketahui bahwa ada 18 bayi yang gemar memakan pisang, 25 bayi gemar makan bubur, dan 9 bayi menyukai keduanya. Lalu ada berapa bayi yang tidak menyukai pisang dan bubur?

Pembahasan:

n{AΛB} = (n{A} + n{B}) - (n{S} - n{X})
9 = (18 + 25) - (40 - n{X})
9 = 43 - 40 + n{X}
9 = 3 + n{X}
9 - 3 = n{X} 
n{X} = 6


Contoh Soal 5:

Dari sekelompok atlet diketahui bahwa 17 orang menyukai sepak bola, 13 menyukai renang, dan 12 orang menyukai keduanya. coba kalian gambarkan diagram venn dan tentukan pula jumlah keseluruhan dari atlet tersebut.

Pembahasan:

Jumlah keseluruhan dari atlet tersebt adalah:
Atlet ang menyukai sepakbola saja : 17-12 = 5 orang
Atlet yang menyukai renang saja = 13 – 12 = 1 orang

Diagram venn-nya adalah:

Contoh Soal Himpunan Matematika dan Pembahasannya Kelas 7 SMP


Jadi, jumlah keseluruhan atlet tersebut adalah 18 orang


Demikian adalah beberapa Contoh Soal Himpunan Matematika dan Pembahasannya khusus untuk kalian yang masih duduk di Kelas 7 SMP. Smoga dapat membantu kalian untuk lebih memahami tentang materi himpunan yang diajarkan oleh guru kalian. Semangat Belajar!!

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Materi Refleksi atau Pencerminan pada Bangun Datar Kelas 5 SD

Pencerminan Bangun Datar Apakah kalian pernah bercermin? Tentu saja kalian pernah bercermin. Nah, ketika kalian bercermin, pasti kalian dapat melihat bayangan wajah atau tubuh kalian pada cermin tersebut. Namun, apabila kalian perhatikan, bayangan yan ada dicermin posisinya terbalik. Tangan kanan kalian akan tampak menjadi tangan kiri di cermin, begitupun sebaliknya tangan kiri kalian akan tampak seperti tangan kanan pada cermin tersebut. Mengapa demikian? Materi Rumus Matematika Dasar kali ini akan membahas mengenai hal tersebut.

Materi Refleksi atau Pencerminan pada Bangun Datar Kelas 5 SD

Materi kali ini berkaitan dengan pencerminan pada bangun datar. Pencerminan atau biasa disebut refleksi pada bangun datar merupakan sebuah transformasi atau perpindahan suatu titik pada bangun datar dengan menggunakan sifat benda dan bayangannya pada sebuah cermin datar. Oleh karenanya, kalian harus paham terlebih dahulu mengenai sifat-sifat pencerminan pada bangun datar yang akan dijelaskan sebagai berikut:

Sifat-Sifat Pencerminan Pada Bangun Datar


Dari gambar yang ada di atas, kita dapat menyimpulkan sifat pencerminan sebagai berikut:
  • Objek dan bayangan akan selalu sama
  • Jarak setiap titik yang ada pada objek terhadap cermin, sama persis dengan jarak setiap titik yang ada pada bayangan terhadap cermin. (s=s')
  • Tinggi bayangan akan sama dengan tinggi bayangannya (h=h')
  • Garis yang menghubungkan tiap titik pada objek dengan titik yang ada pada bayangan akan selalu tegak lurus terhadap cermin.
Sekarang coba perhatikan contoh pencerminan bangun datar berikut ini:

Materi Refleksi atau Pencerminan pada Bangun Datar Kelas 5 SD

Dari gambar tersebut kita dapat melihat sifat-sifat pencerminan sebagai berikut:
  • Luas segitiga PQR = Luas Segitiga P'Q'R' karena Segitiga PQR kongruen dengan Segitiga P',Q',R'
  • RA = R'A, PB = P'B, dan QC = Q'C artinya, jarak titik pada setiap sudut segitiga PQR terhadap cermin sama persis dengan jaraik titik pada setiap sudut segitiga P'Q'R' terhadap cermin.
  • Tinggi segitiga PQR sama dengan tinggi bayangannya (segitiga P'Q'R')
  • Ruas garis PP', QQ', dan RR' tegak lurus terhadap garis cermin AC


Melukis Bayangan Hasil Pencerminan Suatu Bangun Datar

Sebuah bangun dengan empat sisi ABCD dicerminkan terhadap cermin c. Perhatikan gambar dibawah ini serta langkah-langkah untuk melukis bayangannya.

Materi Refleksi atau Pencerminan pada Bangun Datar Kelas 5 SD

  • Tahap pencerminan:
  • Buatlah garis dari titik C, memotong garis c tegak lurus di P.
  • Ukur CP = PC'
  • Buat garis dari titik B memotong garis c tegak lurus di Q.
  • Ukur BQ = QB'
  • Buat garis titik A memotong c tegak lurus di R
  • Ukur AR = RA'
  • Buat garis dari titik D memotong garis c tegak lurus di S
  • Ukur DS = SD'

Hubungkan masing-masing titik A', B', C', dan D'. Maka akan terbentuk segi empat A'B'C'D'. Selanjutnya, dapat kita katakan bahwa segi empat ABCD simetris dengan segiempat A'B'C'D' untuk membuktikanya silahkan kalian ukur kedua segiempat di atas dengan menggunakan penggaris. Apakah ukuran tiap sisi pada segiempat ABCD sama dengan tiap sisi pada segiempat A'B'C'D'?


Cukup sekian materi mengenai Refleksi atau Pencerminan pada Bangun Datar Kelas 5 SD yang dapat disampaikan oleh Rumus Matematika Dasar. Untuk artikel selanjutnya, mungkin akan dibahas contoh-contoh soal mengenai pencerminan bangun datar. So, simak terus artikel terbaru mengenai pelajaran matematika yang ada di blog ini. Sampai jumpa pada materi selanjutnya!!

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Tips Cara Mudah Menghafal Rumus Trigonometri Sudut Ber-relasi

Rumus Trigonometri Sudut Ber-relasi - Untuk dapat memahami nilai perbandingan trigonometri dari suatu sudut, sebaiknya kalian mempelajari konsep sudut ber-relasi. Apabila sudut tersebut adalah sudut istimewa maka kita akan lebih mudah untuk bisa menentukan nilai perbandingan trigonometri dari sudut tersebut. Namun, apabila sudut itu bukanlah termasuk kedalam sudut istimewa kita juga tetap bisa menemukan perbandingan trigonometrinya dengan menggunakan prinsip-prinsip di dalam sudut ber-relasi. Coba perhatikan identitas trigonometri berikut ini:

Tips Cara Mudah Menghafal Rumus Trigonometri Sudut Ber-relasi

Rumus Trigonometri Sudut Ber-relasi

Ada beberapa rumus yang dapat digunakan untuk menentukan perbandingan trigonometri pada sudut ber-relasi (sudut dari kuadran I sampai IV). pada artikel kali ini rumus matematika dasar tidak akan menjelaskan rumus-rumus tersebut satu-persatu karena di sini kita hanya akan belajar tentang cara mudah menghafal rumus-rumus tersebut. seperti kita ketahui bahwa rumus trigonometri untuk sudut ber-relasi terdiri dari (900 ± a0), (1800± a0), (2700 ± a0), (n.3600 ± a0), dan (- a0)

Sekarang mari kita anggap sudut 900, 1800, 2700, dan 3600 mewakili tiap kuadran yang ada, jadi:

900 untuk kuadran I
1800 untuk kuadran II
2700 untuk kuadran III
3600 untuk kuadran IV



Pola Relasi Sudut

Ketika kita berurusan dengan sudut-sudut yang mewakili area kuadran I dan III (kuadran ganjil) maka untuk menentukan nilai perbandingan trigonometri sudut lain dengan menggunakan rumus (900 ± a0), dan (2700 ± a0). Sehingga berlakulah:

sin = cos
cos = sin
cosec = sec
sec = cosec
tan = cotan
cotan = tan

Sementara itu, ketika kita menggunakan sudut yang mewakili area kuadran II dan IV (kuadran genap) maka untuk menentukan nilai perbandingan trigonometri sudut lain dengan menggunakan rumus (1800 ± a0), dan (n.3600 ± a0) berlakulah:

sin = sin
cos =cos
cosec = cosec
sec = sec
tan = tan
cotan = cotan

Catatan: tanda positif dan negatif pada nilai trigonometrinya disesuaikan dengan aturan ASTC.


Apakah yang dimaksud dengan ASTC?
ASTC adalah singkatan yang dibuat untuk mempermudah dalam menghafal nilai positif dan negatif pada trigonometri. AST adalah All, Sinus, Tangen, dan Cosinus. A mewakili kuadran I, S mewaikil Kuadran II, T mewakili kuadran III, dan C mewakili kuadran IV. Dapat juga dituliskan sebagai berikut:

All - I = artinya, pada kuadran I semua nilai trigonometri bernilai positif.
Sinus - II = Artinya pada kuadran II hanya nilai Sinus dan Cosecan yang memiliki nilai positif.
Tangen - III = Artinya pada kuadran III hanya nilai tangen dan cotangen yang memiliki nilai positif.
Cosinus - IV = Artinya pada kuadran IV hanya nilai Cosinus can Secan yang memiliki nilai positif.


Contoh Soal 1:
Coba nyatakan perbandingan beberapa trigonometri berikut ini dalam perbandingan trigonometri sudut relasinya:

A. Sin 540
B. Cos 1350

Pembahasan:

A. Sin 540berada pada kuadran I => nilai sin-nya positif (+)
Sin 540 = (900 - 360)
Maka sin 540 = sin (900- 360)
Sin 540 = cos 360
Karena pada (90 - a) berlaku aturan sin=cos



B.1350berada pada kuadran II => nilai cos-nya negatif karena pada kuadran ini hanya Sinus dan Cosecan yang bernilai positif.

1350= (900 + 450) = (1800 - 450)

Karena pada (900 + a0) berlaku aturan cos = sin
Maka cos 1350= -sin 450

Karena pada (1800 - a0) berlaku aturan cos = cos
Maka cos 1350= cos (1800 - 450)
Cos 1350= -cos 450

Demikianlah Tips Cara Mudah Menghafal Rumus Trigonometri Sudut Ber-relasi semoga artikel yang diberikan oleh rumus matematika dasar di atas bisa bermanfaat.

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Penjelasan Perbedaan Permutasi dan Kombinasi Matematika, Contoh Soal dan Pembahasan Lengkap

Permutasi dan Kombinasi Matematika - Pelajaran matematika mengenai permutasi dan kombinasi  diajarkan pada siswa-siswi yang duduk di kelas XI SMA. Materi ini masih berkaitan dengan Peluang. Lalu apa bedanya peluang, permutasi dan kombinasi? Tenang, jangan terburu-buru. Pada artikel ini Rumus Matematika Dasar akan menjabarkan satu-persatu kepada kalian mengenai permutasi dan kombinasi dalam matematika. Sedangkan untuk materi peluang dapat kalian akses pada artikel yang membahas tentang Pengertian dan Rumus Peluang Matematika.


Seperti biasa, di sini kalian tidak hanya memperoleh penjelasan materi namun juga rumus serta contoh-sontoh soal dan penjelasan mengenai langkah-langkah dalam menjawab soal tersebut. Oleh karenanya, kalian harus memperhatikan dengan baik uraian materi serta penjelasan rumus yang diberikan.


Pengertian Permutasi dan Kombinasi Matematika


Permutasi

Di dalam ilmu matematika permutasi diartikan sebagai sebuah konsep penyusunan sekumpulan objek/angka menjadi beberapa urutan berbeda tanpa mengalami pengulangan.

Di dalam permutasi, urutan sangat diperhatikan. setiap objek yang dihasilkan harus berbeda antara satu dengan yang lain. kita ambil contoh, urutan huruf ({ABC} berbeda dengan {CAB} begitu juga dengan {BAC) dan {ACB}). Rumus untuk mencari banyaknya permutasi n unsur jika disusun pada unsur k di mana k ≤ n adalah:

Rumus Permutasi

P(n,k) =   n!  
     (n-k)!


Untuk memahami rumus tersebut, perhatikan pembahasan soal di bawah ini:


Contoh Soal 1
Di sebuah sekolah ada 4 orang guru yang dicalonkan untuk mengisi posisi bendahara dan sekertaris. Coba kalian tentukan banyaknya cara yang dapat digunakan untuk mengisi posisi tersebut!

Pembahasan:
Soal di atas dapat dituliskan sebagai permutasi P(4,2), n(banyaknya guru) = 4 k (jumlah posisi) = 2
masukkan ke dalam rumus:

P(4,2) =   4!     = 4 x 3 x 2 x 1 = 24 = 12
 (4-2)!           2 x 1             2


Contoh Soal 2
Berapakah banyaknya bilangan yang dibentuk dari 2 angka berbeda yang dapat kita susun dari urutan angka 4, 8, 2, 3, dan 5?

Pembahasan:
pertanyaan di atas dapat disimpulkan sebagai permutasi yang terdiri dari 2 unsur yang dipilih dari 5 unsur maka dapat dituliskan sebagai P(5,2). tinggal kita masukkan ke dalam rumus.

P(5,2) =   5!     = 5x 4 x 3 x 2 x 1 = 120 = 20
              (5-2)!        3 x 2 x 1              6

Maka ada 20 cara yang dapat dilakukan untuk menysyn bilangan tersebut menjadi 2 angka yang berbeda-beda (48, 42, 43, 45, 84, 82, 83, 85, 24, 28, 23, 25, 34, 38, 32, 35, 54, 58, 53, 52).


Kombinasi

kombinasi merupakan sebuah kumpulan dari sebagian atau seluruh objek dengan tidak memperhatikan urutannya. di dalam kombinasi, {AB} dianggap sama dengan {BA} sehingga sebuah kombinasi dari dua objek yang sama tidak dapat terulang.

Rumus kombinasi dari suatu himpunan yang mempunyai n elemen dapat dituliskan sebagai berikut:

Rumus Kombinasi

C(n,r) = nCr= nCr    n!     
                                  r!(n-r)!

Mari kita amati penggunaan rumus tersebut untuk menyelesaikan soal-soal di bawah ini:


Contoh Soal 3
Manuel Pelegrini membawa 16 pemain saat Manchester City melawan Liverpool di Etihad Stadium. 11 orang diantaranya akan dipilih untuk bermain pada babak pertama. jika kita tidak memperhatikan posisi pemain, berapakah banyaknya cara yang dapat diambil oleh pelatih untuk memilih pemain?

Pembahasan:
Karena tidak mementingkan posisi pemain, maka kita gunakan rumus kombinasi:
16C11       16!        =  16 x 15 x 14 x 13 x 12 x 11!  
              11!(16-11)!                      11!5!                          

         524160         =  524160  = 4368
     5 x 4 x 3 x 2 x 1          120


Contoh Soal 4

Sebuah ember berisi 1 buah alpukat, 1 buah pir, 1 buah jeruk dan 1 buah salak. berapakah banyaknya kombinasi yang tersusun dari 3 macam buah?

Pembahasan:
diketahui n = 4 dan r = 3, maka:

4C      4!        =  4 x 3 x 2 x 1  =      24         =  24  = 4
              3!(4-3)!           3!1!              3 x 2 x 1         6


Baiklah, sekarang pasti kalian sudah mengerti tentang sampai di sini dulu pembahasan materi Perbedaan Permutasi dan Kombinasi Matematika, Contoh Soal dan Pembahasan Lengkap untuk kesempatan ini. Silahkan simak materi pelajaran matematika lainnya yang ada di blog ini untuk menambah wawasan kalian seputar ilmu matematika.

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Materi Pengertian dan Rumus Peluang Matematika SMP Terlengkap

Pengertian dan Rumus Peluang Matematika - Apakah kalian pernah bermain ular tangga? Di dalam permainan ular tangga tentu kalian akan menggunakan dadu untuk menentukan jumlah langkah yang harus kalian ambil. Pada proses pelemparan dadu, hasil atau angka yang mungkin muncil adalah 1,2,3,4,5, atau 6. Nah kemungkinan munculnya angka pada saat melempar dadu adalah salah satu contoh Peluang Matematika.

Materi Pengertian dan Rumus Peluang Matematika SMP Terlengkap

Contoh lain dari peluang matematika adalah pelemparan koin. Pada saat melempar koin ada dua buah kemungkinan sisi yang muncul. Sisi yang pertama adalah angka (A) dan sisi yang kedua adalah gambar (A). Nah, pada materi kali ini, rumus matematika dasar akan memberikan rangkuman materi mengenai pengertian dan rumus peluang dalam matematika.  Mari kita simak rangkuman materinya sebagai berikut:


Memahami Definisi dan Rumus Peluang dalam Matematika


Definisi Peluang
Peluang dapat didefinisikan sebagai sebuah cara yang dilakukan untuk mengetahui kemungkinan terjadinya sebuah peristiwa.

Di dalam materi mengenai peluang, dikenal beberapa istilah yang sering digunakan, seperti:

Ruang Sampel
Merupakan himpunan dari semua hasil percobaan yang mungkin terjadi.

Titik Sampel
Merupakan anggota yang ada di dalam ruang sampel

Kejadian
Merupakan himpunan bagian dari ruang sampel.


RUMUS PELUANG MATEMATIKA

Frekuensi merupakan perbandingan antara banyaknya percobaan yang dilakukan dengan banyaknya kejadian yang diamati. Frekuensi dapat diketahui dengan menggunakan rumus:




Apabila setiap titik sampel dari anggota ruang sampel S mempunyai peluang yang sama, maka peluang kejadian K yang jumlah anggotanya dinyatakan dalam n(K) dapat diketahui dengan rumus :




Peluang munculnya kejadian dapat diperkirakan melalui notasi di bawah ini:


Apabila nilai P(K) = 0 maka kejadian K tersebut sangat mustahil untuk terjadi

Apabila nilai P(K) = 1 maka kejadian K tersebut pasti akan terjadi


Amatilah contoh soal di bawah ini:

Contoh Soal 1
Pada proses pelemparan sebuah dadu, tentukanlah peluang munculnya mata dadu yang berangka ganjil

Jawab:
Ruang sampel S = {1,2,3,4,5,6}
n(S) = 6

Mata dadu ganjil = {1,3,5}
n(S) = 3

maka P(K) = 3/6 = 1/2



Kejadian Majemuk

Kejadian majemuk adalah dua atau lebih kejadian yang dioperasikan sehingga terbentuklah sebuah kejadian yang baru

Suatu kejadian K dan kejadian komplemen berupa K' memenuhi persamaan:

P(K) + P(K') = 1 atau P(K') = 1 - P(K)


Contoh Soal 2
dari seperangkat kartu bridge, diambillah satu buah kartu secara acak. tentukan peluang terambilnya kartu yang bukan As.

Jawab:
jumlah kartu bridge = n(S) = 52
jumlah kartu As = n(K) = 4
P(K) = 4/52 = 1/13

peluang yang terambil bukan kartu As = P(K') = 1-P(K) = 1 - 1/13 = 12/13


PENJUMLAHAN PELUANG


Kejadian Saling Lepas
dua buah kejadian A dan B dikatakan saling lepas apabila tak ada satupun elemen pada kejadian A yang sama dengan elemen yang ada pada kejadian B. untuk dua buah kejadian yang saling lepas, maka peluang salah satu A atau B mungkin terjadi, rumusnya adalah:

P(A u B) = P(A) + P(B)


Contoh Soal 3
Dua buah dadu masing-masing berwarna merah dan putih dilempar secara bersamaan sebanyak satu kali, tentukanlah peluang munculnya mata dadu yang berjumlah 3 atau 10!

Jawab:
Hasil pelemparan dadu tersebut dapat digambarkan dengan tabel ini:

Materi Pengertian dan Rumus Peluang Matematika SMP


Kejadian mata dadu berjumlah 3 ditandai dengan warna kuning.
A = {(1,2), (2,1)}
n(A) = 2

Kejadian mata dadu berjumlah 10 ditandai dengan warna biru
B = {(4,6), (5,5), (6,4)}

Karena tidak ada elemen yang sama pada A dan B digunakan rumus:

P(A u B) = P(A) + P(B)
P(A u B) = 2/36 + 3/36
P(A u B) = 5/36



Kejadian Tidak Saling Lepas
Artinya ada elemen A yang sama dengan elemen B, rumusnya dapat dituliskan menjadi:


P(A u B) = P(A) + P(B) - P(A n B)


Contoh Soal 4
Sebuah kartu diambil dari tumpukkan kartu bridge secara acak. coba kalian tentukan peluang dari kartu yang terambil adalah kartu hati dan kartu bergambar (K,Q,J)!

Jawab:
Jumlah kartu bridge = n(S) = 52
jumlah kartu hati = n(A) = 13
jumlah kartu bergambar = n(B) = 12

karena ada kartu bergambar yang merupakan kelompok kartu hati (J hati, Q hati, dan K hati) maka A dan B tidak saling lepas sehingga digunakanlah rumus:

P(A u B) = P(A) + P(B) - P(A n B)
= 13/52 + 12/52 - 3/52

= 22/52 = 11/26



Kejadian Saling Bebas
Dua buah kejadian dapat disebut saling bebas bila munculnya kejadian A tidak berpengaruh pada munculnya kejadian B sehingga peluang kejadian A dan B terjadi bersamaan dapat dituliskan menjadi:

P(A n B) = P(A) x P(B)


Contoh Soal 5
Pada percobaan pelemparan dua buah dadu, coba tentukan peluang munculnya angka genap pada dau pertama dan angka ganjil prima pada dadu kedua!

Jawab:
misalkan A = kejadian munculnya mata dadu genap pada dadu pertama = {2,4,6} maka P(A) = 3/6

misalkan B = kejadian munculnya mata dadu ganjil prima pada dadu kedua = {3,5} maka P(B) = 2/6

karena kejadian A tidak berpengaruh pada kejadian B maka digunakan rumus:

P(A n B) = P(A) x P(B)
P(A n B) = 3/6 x 2/6 = 1/6



Kejadian Bersyarat
kejadian bersyarat terjaid apabila kejadian A mempengaruhi munculnya kejadian B atau sebaliknya. maka dapat dituliskan seperti ini:

P(A n B) = P(A) x P(B/A)

atau

P(A n B) = P(B) x P(A/B)


Contoh Soal 6
ada sebuah kotak yang berisi 5 bola merah dan 4 bola hijau. bila diambil dua buah bola satu persatu tanpa adanya pengembalian, tentukanlah peluang bola yang terambil adalah bola merah pada pengambilan pertama dan bola hijau pada pengambilan kedua!

Jawab:
Pada pengambilan pertama tersedia 5 bola merah dari 9 bola yang ada.
maka P(M) = 5/9

Pada pengambilan kedua ada 4 bola hijau dari 8 bola yang tersisa (dengan syarat bola merah telah terambil).
maka P(H/M) = 4/8

karena kejadiannya saling berpengaruh, digunakanlah rumus:

P(M n H) = P(M) x P(H/M)
P(M n H) = 5/9 x 4/8 = 5/18


Demikianlah penjelasan lengkap Materi Pengertian dan Rumus Peluang Matematika SMP. Selamat belajar dan semoga dapat memahami materi yang diberikan dengan baik. Simak materi lainnya yang ada di blog ini seperti Pengertian Fungsi dan Macam-macam Fungsi dalam Matematika

Related Posts:

Gambar Tabel Logaritma Matematika Lengkap

Gambar Tabel Logaritma - Tabel logaritma adalah sebuah tabel yang berisi nilai-nilai logaritma dari bilangan-bilangan tertentu. Tabel logaritma dapat membantu kalian dalam mengerjakan soal-soal yang berkaitan dengan persamaan logaritma. sesungguhnya kita bisa menghitung nilai logaritma secara manual, akan tetapi untuk mengecek kebenaran dari hasil penghitungan tersebut kita terkadang membutuhkan tabel logaritma. 

Gambar Tabel Logaritma Matematika Lengkap


Gambar di atas adalah langkah untuk menggunakan tabel logaritma. misalkan kalian ingin mencari nilai log 1.34 maka pertama-tama kalian harus mencari angka 1.3 pada kolom pertama (N) kemudian angka 4 pada baris pertama yang berpotongan dengan baris 1.3. maka itulah hasil logaritmanya (0.1271).

Rumus Matematika Dasar sengaja memberikan tabel logaritma sebagai alat bantu kalian dalam mempelajari matematika. tabel logaritma ini merupakan table logaritma dari 1-10. silahkan kalian lihat langsung tabelnya di bawah ini atau kalian juga bisa mendownloadnya dalam bentuk pdf pada link yang telah disediakan.

Gambar Tabel Logaritma Matematika 1 sampai 10  Lengkap



N0123456789
10
1.01
1.020.01030.0107240.0111470.011570.0119930.012415
1.030.0128370.0132590.013680.01410.0145210.014940.015360.0157790.0161970.016616
1.040.0170330.0174510.0178680.0182840.01870.0191160.0195320.0199470.0203610.020775
1.050.0211890.0216030.0220160.0224280.0228410.0232520.0236640.0240750.0244860.024896
1.060.0253060.0257150.0261250.0265330.0269420.027350.0277570.0281640.0285710.028978
1.070.0293840.0297890.0301950.03060.0310040.0314080.0318120.0322160.0326190.033021
1.080.0334240.0338260.0342270.0346280.0350290.035430.035830.036230.0366290.037028
1.090.0374260.0378250.0382230.038620.0390170.0394140.0398110.0402070.0406020.040998
N0123456789
1.10.0413930.0417870.0421820.0425760.0429690.0433620.0437550.0441480.044540.044932
1.110.0453230.0457140.0461050.0464950.0468850.0472750.0476640.0480530.0484420.04883
1.120.0492180.0496060.0499930.050380.0507660.0511530.0515380.0519240.0523090.052694
1.130.0530780.0534630.0538460.054230.0546130.0549960.0553780.055760.0561420.056524
1.140.0569050.0572860.0576660.0580460.0584260.0588050.0591850.0595630.0599420.06032
1.150.0606980.0610750.0614520.0618290.0622060.0625820.0629580.0633330.0637090.064083
1.160.0644580.0648320.0652060.065580.0659530.0663260.0666990.0670710.0674430.067815
1.170.0681860.0685570.0689280.0692980.0696680.0700380.0704070.0707760.0711450.071514
1.180.0718820.072250.0726170.0729850.0733520.0737180.0740850.0744510.0748160.075182
1.190.0755470.0759120.0762760.076640.0770040.0773680.0777310.0780940.0784570.078819
N0123456789
1.20.0791810.0795430.0799040.0802660.0806260.0809870.0813470.0817070.0820670.082426
1.210.0827850.0831440.0835030.0838610.0842190.0845760.0849340.0852910.0856470.086004
1.220.086360.0867160.0870710.0874260.0877810.0881360.088490.0888450.0891980.089552
1.230.0899050.0902580.0906110.0909630.0913150.0916670.0920180.092370.0927210.093071
1.240.0934220.0937720.0941220.0944710.094820.0951690.0955180.0958660.0962150.096562
1.250.096910.0972570.0976040.0979510.0982980.0986440.098990.0993350.0996810.100026
1.260.1003710.1007150.1010590.1014030.1017470.1020910.1024340.1027770.1031190.103462
1.270.1038040.1041460.1044870.1048280.1051690.105510.1058510.1061910.1065310.106871
1.280.107210.1075490.1078880.1082270.1085650.1089030.1092410.1095790.1099160.110253
1.290.110590.1109260.1112630.1115990.1119340.112270.1126050.112940.1132750.113609
N0123456789
1.30.1139430.1142770.1146110.1149440.1152780.1156110.1159430.1162760.1166080.11694
1.310.1172710.1176030.1179340.1182650.1185950.1189260.1192560.1195860.1199150.120245
1.320.1205740.1209030.1212310.121560.1218880.1222160.1225440.1228710.1231980.123525
1.330.1238520.1241780.1245040.124830.1251560.1254810.1258060.1261310.1264560.126781
1.340.1271050.1274290.1277530.1280760.1283990.1287220.1290450.1293680.129690.130012
1.350.1303340.1306550.1309770.1312980.1316190.1319390.132260.132580.13290.133219
1.360.1335390.1338580.1341770.1344960.1348140.1351330.1354510.1357690.1360860.136403
1.370.1367210.1370370.1373540.1376710.1379870.1383030.1386180.1389340.1392490.139564
1.380.1398790.1401940.1405080.1408220.1411360.141450.1417630.1420760.1423890.142702
1.390.1430150.1433270.1436390.1439510.1442630.1445740.1448850.1451960.1455070.145818
N0123456789
1.40.1461280.1464380.1467480.1470580.1473670.1476760.1479850.1482940.1486030.148911
1.410.1492190.1495270.1498350.1501420.1504490.1507560.1510630.151370.1516760.151982
1.420.1522880.1525940.15290.1532050.153510.1538150.154120.1544240.1547280.155032
1.430.1553360.155640.1559430.1562460.1565490.1568520.1571540.1574570.1577590.158061
1.440.1583620.1586640.1589650.1592660.1595670.1598680.1601680.1604690.1607690.161068
1.450.1613680.1616670.1619670.1622660.1625640.1628630.1631610.163460.1637580.164055
1.460.1643530.164650.1649470.1652440.1655410.1658380.1661340.166430.1667260.167022
1.470.1673170.1676130.1679080.1682030.1684970.1687920.1690860.169380.1696740.169968
1.480.1702620.1705550.1708480.1711410.1714340.1717260.1720190.1723110.1726030.172895
1.490.1731860.1734780.1737690.174060.1743510.1746410.1749320.1752220.1755120.175802
N0123456789
1.50.1760910.1763810.176670.1769590.1772480.1775360.1778250.1781130.1784010.178689
1.510.1789770.1792640.1795520.1798390.1801260.1804130.1806990.1809860.1812720.181558
1.520.1818440.1821290.1824150.18270.1829850.183270.1835550.1838390.1841230.184407
1.530.1846910.1849750.1852590.1855420.1858250.1861080.1863910.1866740.1869560.187239
1.540.1875210.1878030.1880840.1883660.1886470.1889280.1892090.189490.1897710.190051
1.550.1903320.1906120.1908920.1911710.1914510.191730.192010.1922890.1925670.192846
1.560.1931250.1934030.1936810.1939590.1942370.1945140.1947920.1950690.1953460.195623
1.570.19590.1961760.1964530.1967290.1970050.1972810.1975560.1978320.1981070.198382
1.580.1986570.1989320.1992060.1994810.1997550.2000290.2003030.2005770.200850.201124
1.590.2013970.201670.2019430.2022160.2024880.2027610.2030330.2033050.2035770.203848
N0123456789
1.60.204120.2043910.2046630.2049340.2052040.2054750.2057460.2060160.2062860.206556
1.610.2068260.2070960.2073650.2076340.2079040.2081730.2084410.208710.2089790.209247
1.620.2095150.2097830.2100510.2103190.2105860.2108530.2111210.2113880.2116540.211921
1.630.2121880.2124540.212720.2129860.2132520.2135180.2137830.2140490.2143140.214579
1.640.2148440.2151090.2153730.2156380.2159020.2161660.216430.2166940.2169570.217221
1.650.2174840.2177470.218010.2182730.2185360.2187980.219060.2193230.2195850.219846
1.660.2201080.220370.2206310.2208920.2211530.2214140.2216750.2219360.2221960.222456
1.670.2227160.2229760.2232360.2234960.2237550.2240150.2242740.2245330.2247920.225051
1.680.2253090.2255680.2258260.2260840.2263420.22660.2268580.2271150.2273720.22763
1.690.2278870.2281440.22840.2286570.2289130.229170.2294260.2296820.2299380.230193
N0123456789
1.70.2304490.2307040.230960.2312150.231470.2317240.2319790.2322340.2324880.232742
1.710.2329960.233250.2335040.2337570.2340110.2342640.2345170.234770.2350230.235276
1.720.2355280.2357810.2360330.2362850.2365370.2367890.2370410.2372920.2375440.237795
1.730.2380460.2382970.2385480.2387990.2390490.2392990.239550.23980.240050.2403
1.740.2405490.2407990.2410480.2412970.2415460.2417950.2420440.2422930.2425410.24279
1.750.2430380.2432860.2435340.2437820.244030.2442770.2445250.2447720.2450190.245266
1.760.2455130.2457590.2460060.2462520.2464990.2467450.2469910.2472370.2474820.247728
1.770.2479730.2482190.2484640.2487090.2489540.2491980.2494430.2496870.2499320.250176
1.780.250420.2506640.2509080.2511510.2513950.2516380.2518810.2521250.2523680.25261
1.790.2528530.2530960.2533380.253580.2538220.2540640.2543060.2545480.254790.255031
N0123456789
1.80.2552730.2555140.2557550.2559960.2562370.2564770.2567180.2569580.2571980.257439
1.810.2576790.2579180.2581580.2583980.2586370.2588770.2591160.2593550.2595940.259833
1.820.2600710.260310.2605480.2607870.2610250.2612630.2615010.2617390.2619760.262214
1.830.2624510.2626880.2629250.2631620.2633990.2636360.2638730.2641090.2643460.264582
1.840.2648180.2650540.265290.2655250.2657610.2659960.2662320.2664670.2667020.266937
1.850.2671720.2674060.2676410.2678750.268110.2683440.2685780.2688120.2690460.269279
1.860.2695130.2697460.269980.2702130.2704460.2706790.2709120.2711440.2713770.271609
1.870.2718420.2720740.2723060.2725380.272770.2730010.2732330.2734640.2736960.273927
1.880.2741580.2743890.274620.274850.2750810.2753110.2755420.2757720.2760020.276232
1.890.2764620.2766920.2769210.2771510.277380.2776090.2778380.2780670.2782960.278525
N0123456789
1.90.2787540.2789820.2792110.2794390.2796670.2798950.2801230.2803510.2805780.280806
1.910.2810330.2812610.2814880.2817150.2819420.2821690.2823960.2826220.2828490.283075
1.920.2833010.2835270.2837530.2839790.2842050.2844310.2846560.2848820.2851070.285332
1.930.2855570.2857820.2860070.2862320.2864560.2866810.2869050.287130.2873540.287578
1.940.2878020.2880260.2882490.2884730.2886960.288920.2891430.2893660.2895890.289812
1.950.2900350.2902570.290480.2907020.2909250.2911470.2913690.2915910.2918130.292034
1.960.2922560.2924780.2926990.292920.2931410.2933630.2935840.2938040.2940250.294246
1.970.2944660.2946870.2949070.2951270.2953470.2955670.2957870.2960070.2962260.296446
1.980.2966650.2968840.2971040.2973230.2975420.2977610.2979790.2981980.2984160.298635
1.990.2988530.2990710.2992890.2995070.2997250.2999430.3001610.3003780.3005950.300813
N0123456789
20.301030.3012470.3014640.3016810.3018980.3021140.3023310.3025470.3027640.30298
2.010.3031960.3034120.3036280.3038440.3040590.3042750.3044910.3047060.3049210.305136
2.020.3053510.3055660.3057810.3059960.3062110.3064250.3066390.3068540.3070680.307282
2.030.3074960.307710.3079240.3081370.3083510.3085640.3087780.3089910.3092040.309417
2.040.309630.3098430.3100560.3102680.3104810.3106930.3109060.3111180.311330.311542
2.050.3117540.3119660.3121770.3123890.31260.3128120.3130230.3132340.3134450.313656
2.060.3138670.3140780.3142890.3144990.314710.314920.315130.315340.3155510.31576
2.070.315970.316180.316390.3165990.3168090.3170180.3172270.3174360.3176460.317854
2.080.3180630.3182720.3184810.3186890.3188980.3191060.3193140.3195220.319730.319938
2.090.3201460.3203540.3205620.3207690.3209770.3211840.3213910.3215980.3218050.322012
N0123456789
2.10.3222190.3224260.3226330.3228390.3230460.3232520.3234580.3236650.3238710.324077
2.110.3242820.3244880.3246940.3248990.3251050.325310.3255160.3257210.3259260.326131
2.120.3263360.3265410.3267450.326950.3271550.3273590.3275630.3277670.3279720.328176
2.130.328380.3285830.3287870.3289910.3291940.3293980.3296010.3298050.3300080.330211
2.140.3304140.3306170.3308190.3310220.3312250.3314270.331630.3318320.3320340.332236
2.150.3324380.332640.3328420.3330440.3332460.3334470.3336490.333850.3340510.334253
2.160.3344540.3346550.3348560.3350570.3352570.3354580.3356580.3358590.3360590.33626
2.170.336460.336660.336860.337060.337260.3374590.3376590.3378580.3380580.338257
2.180.3384560.3386560.3388550.3390540.3392530.3394510.339650.3398490.3400470.340246
2.190.3404440.3406420.3408410.3410390.3412370.3414350.3416320.341830.3420280.342225
N0123456789
2.20.3424230.342620.3428170.3430140.3432120.3434090.3436060.3438020.3439990.344196
2.210.3443920.3445890.3447850.3449810.3451780.3453740.345570.3457660.3459620.346157
2.220.3463530.3465490.3467440.3469390.3471350.347330.3475250.347720.3479150.34811
2.230.3483050.34850.3486940.3488890.3490830.3492780.3494720.3496660.349860.350054
2.240.3502480.3504420.3506360.3508290.3510230.3512160.351410.3516030.3517960.351989
2.250.3521830.3523750.3525680.3527610.3529540.3531470.3533390.3535320.3537240.353916
2.260.3541080.3543010.3544930.3546850.3548760.3550680.355260.3554520.3556430.355834
2.270.3560260.3562170.3564080.3565990.356790.3569810.3571720.3573630.3575540.357744
2.280.3579350.3581250.3583160.3585060.3586960.3588860.3590760.3592660.3594560.359646
2.290.3598350.3600250.3602150.3604040.3605930.3607830.3609720.3611610.361350.361539
N0123456789
2.30.3617280.3619170.3621050.3622940.3624820.3626710.3628590.3630480.3632360.363424
2.310.3636120.36380.3639880.3641760.3643630.3645510.3647390.3649260.3651130.365301
2.320.3654880.3656750.3658620.3660490.3662360.3664230.366610.3667960.3669830.367169
2.330.3673560.3675420.3677290.3679150.3681010.3682870.3684730.3686590.3688450.36903
2.340.3692160.3694010.3695870.3697720.3699580.3701430.3703280.3705130.3706980.370883
2.350.3710680.3712530.3714370.3716220.3718060.3719910.3721750.372360.3725440.372728
2.360.3729120.3730960.373280.3734640.3736470.3738310.3740150.3741980.3743820.374565
2.370.3747480.3749320.3751150.3752980.3754810.3756640.3758460.3760290.3762120.376394
2.380.3765770.3767590.3769420.3771240.3773060.3774880.377670.3778520.3780340.378216
2.390.3783980.378580.3787610.3789430.3791240.3793060.3794870.3796680.3798490.38003
N0123456789
2.40.3802110.3803920.3805730.3807540.3809340.3811150.3812960.3814760.3816560.381837
2.410.3820170.3821970.3823770.3825570.3827370.3829170.3830970.3832770.3834560.383636
2.420.3838150.3839950.3841740.3843530.3845330.3847120.3848910.385070.3852490.385428
2.430.3856060.3857850.3859640.3861420.3863210.3864990.3866770.3868560.3870340.387212
2.440.387390.3875680.3877460.3879230.3881010.3882790.3884560.3886340.3888110.388989
2.450.3891660.3893430.389520.3896980.3898750.3900510.3902280.3904050.3905820.390759
2.460.3909350.3911120.3912880.3914640.3916410.3918170.3919930.3921690.3923450.392521
2.470.3926970.3928730.3930480.3932240.39340.3935750.3937510.3939260.3941010.394277
2.480.3944520.3946270.3948020.3949770.3951520.3953260.3955010.3956760.395850.396025
2.490.3961990.3963740.3965480.3967220.3968960.3970710.3972450.3974190.3975920.397766
N0123456789
2.50.397940.3981140.3982870.3984610.3986340.3988080.3989810.3991540.3993280.399501
2.510.3996740.3998470.400020.4001920.4003650.4005380.4007110.4008830.4010560.401228
2.520.4014010.4015730.4017450.4019170.4020890.4022610.4024330.4026050.4027770.402949
2.530.4031210.4032920.4034640.4036350.4038070.4039780.4041490.404320.4044920.404663
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9.530.9790930.9791380.9791840.979230.9792750.9793210.9793660.9794120.9794570.979503
9.540.9795480.9795940.9796390.9796850.979730.9797760.9798210.9798670.9799120.979958
9.550.9800030.9800490.9800940.980140.9801850.9802310.9802760.9803220.9803670.980412
9.560.9804580.9805030.9805490.9805940.980640.9806850.980730.9807760.9808210.980867
9.570.9809120.9809570.9810030.9810480.9810930.9811390.9811840.9812290.9812750.98132
9.580.9813660.9814110.9814560.9815010.9815470.9815920.9816370.9816830.9817280.981773
9.590.9818190.9818640.9819090.9819540.9820.9820450.982090.9821350.9821810.982226
N0123456789
9.60.9822710.9823160.9823620.9824070.9824520.9824970.9825430.9825880.9826330.982678
9.610.9827230.9827690.9828140.9828590.9829040.9829490.9829940.983040.9830850.98313
9.620.9831750.983220.9832650.983310.9833560.9834010.9834460.9834910.9835360.983581
9.630.9836260.9836710.9837160.9837620.9838070.9838520.9838970.9839420.9839870.984032
9.640.9840770.9841220.9841670.9842120.9842570.9843020.9843470.9843920.9844370.984482
9.650.9845270.9845720.9846170.9846620.9847070.9847520.9847970.9848420.9848870.984932
9.660.9849770.9850220.9850670.9851120.9851570.9852020.9852470.9852920.9853370.985382
9.670.9854260.9854710.9855160.9855610.9856060.9856510.9856960.9857410.9857860.98583
9.680.9858750.985920.9859650.986010.9860550.98610.9861440.9861890.9862340.986279
9.690.9863240.9863690.9864130.9864580.9865030.9865480.9865930.9866370.9866820.986727
N0123456789
9.70.9867720.9868170.9868610.9869060.9869510.9869960.987040.9870850.987130.987175
9.710.9872190.9872640.9873090.9873530.9873980.9874430.9874880.9875320.9875770.987622
9.720.9876660.9877110.9877560.98780.9878450.987890.9879340.9879790.9880240.988068
9.730.9881130.9881570.9882020.9882470.9882910.9883360.9883810.9884250.988470.988514
9.740.9885590.9886040.9886480.9886930.9887370.9887820.9888260.9888710.9889160.98896
9.750.9890050.9890490.9890940.9891380.9891830.9892270.9892720.9893160.9893610.989405
9.760.989450.9894940.9895390.9895830.9896280.9896720.9897170.9897610.9898060.98985
9.770.9898950.9899390.9899830.9900280.9900720.9901170.9901610.9902060.990250.990294
9.780.9903390.9903830.9904280.9904720.9905160.9905610.9906050.990650.9906940.990738
9.790.9907830.9908270.9908710.9909160.990960.9910040.9910490.9910930.9911370.991182
N0123456789
9.80.9912260.991270.9913150.9913590.9914030.9914480.9914920.9915360.991580.991625
9.810.9916690.9917130.9917580.9918020.9918460.991890.9919350.9919790.9920230.992067
9.820.9921110.9921560.99220.9922440.9922880.9923330.9923770.9924210.9924650.992509
9.830.9925540.9925980.9926420.9926860.992730.9927740.9928190.9928630.9929070.992951
9.840.9929950.9930390.9930830.9931270.9931720.9932160.993260.9933040.9933480.993392
9.850.9934360.993480.9935240.9935680.9936130.9936570.9937010.9937450.9937890.993833
9.860.9938770.9939210.9939650.9940090.9940530.9940970.9941410.9941850.9942290.994273
9.870.9943170.9943610.9944050.9944490.9944930.9945370.9945810.9946250.9946690.994713
9.880.9947570.9948010.9948450.9948890.9949330.9949770.9950210.9950650.9951080.995152
9.890.9951960.995240.9952840.9953280.9953720.9954160.995460.9955040.9955470.995591
N0123456789
9.90.9956350.9956790.9957230.9957670.9958110.9958540.9958980.9959420.9959860.99603
9.910.9960740.9961170.9961610.9962050.9962490.9962930.9963370.996380.9964240.996468
9.920.9965120.9965550.9965990.9966430.9966870.9967310.9967740.9968180.9968620.996906
9.930.9969490.9969930.9970370.997080.9971240.9971680.9972120.9972550.9972990.997343
9.940.9973860.997430.9974740.9975170.9975610.9976050.9976480.9976920.9977360.997779
9.950.9978230.9978670.997910.9979540.9979980.9980410.9980850.9981290.9981720.998216
9.960.9982590.9983030.9983470.998390.9984340.9984770.9985210.9985640.9986080.998652
9.970.9986950.9987390.9987820.9988260.9988690.9989130.9989560.9990.9990430.999087
9.980.9991310.9991740.9992180.9992610.9993050.9993480.9993920.9994350.9994790.999522
9.990.9995650.9996090.9996520.9996960.9997390.9997830.9998260.999870.9999130.999957
1011.000041.000091.000131.000171.000221.000261.00031.000351.00039

Itulah Gambar Tabel Logaritma Matematika Lengkap dari 1 sampai 10. Untuk tabel yang lebih lengkap kalian dapat mendownloadnya pada link berikut ini:

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