Roboguru

Dalam sebuah kotak terdapat 7 kelereng berwarna merah dan 5 kelereng berwarna putih. Dari kotak itu diambil 3 kelereng sekaligus secara acak. Peluang terambil sekurang-kurangnya 1 kelereng putih adalah...

Pertanyaan

Dalam sebuah kotak terdapat 7 kelereng berwarna merah dan 5 kelereng berwarna putih. Dari kotak itu diambil 3 kelereng sekaligus secara acak. Peluang terambil sekurang-kurangnya 1 kelereng putih adalah...

  1. begin mathsize 14px style 7 over 44 end style

  2. begin mathsize 14px style 10 over 44 end style

  3. begin mathsize 14px style 34 over 44 end style

  4. begin mathsize 14px style 35 over 44 end style

  5. begin mathsize 14px style 37 over 44 end style

Pembahasan Soal:

Karena syarat terambil sekurang-kurangnya 1 putih, maka terdapat beberapa kemungkinan, yaitu :

- 1 putih dan 2 merah

-2 putih dan 1 merah

- ketiga-tiganya putih

tentukan dulu titik sampelnya begin mathsize 14px style left parenthesis n left parenthesis A right parenthesis right parenthesis end style

1 putih 2 merah :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell C presubscript 5 subscript 1 space x scriptbase space C end scriptbase presubscript 7 subscript 2 end cell row blank equals cell fraction numerator 5 factorial over denominator left parenthesis 5 minus 1 right parenthesis factorial 1 factorial end fraction cross times space fraction numerator 7 factorial over denominator left parenthesis 7 minus 2 right parenthesis factorial 2 factorial end fraction end cell row blank equals cell space fraction numerator 5 factorial over denominator 4 factorial end fraction cross times fraction numerator 7 factorial over denominator 5 factorial 2 factorial end fraction end cell row blank equals cell space fraction numerator 7 factorial over denominator 4 factorial 2 factorial end fraction end cell row blank equals cell space fraction numerator 7 cross times 6 cross times 5 cross times 4 factorial over denominator 4 factorial 2 factorial end fraction end cell row blank equals cell fraction numerator 7 cross times 6 cross times 5 space over denominator 2 end fraction end cell row blank equals 105 end table end style

2 putih dan 1 merah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell C presubscript 5 subscript 2 space x scriptbase space C end scriptbase presubscript 7 subscript 1 end cell row blank equals cell fraction numerator 5 factorial over denominator left parenthesis 5 minus 2 right parenthesis factorial 2 factorial end fraction cross times space fraction numerator 7 factorial over denominator left parenthesis 7 minus 1 right parenthesis factorial 1 factorial end fraction end cell row blank equals cell space fraction numerator 5 factorial over denominator 2 factorial 3 factorial end fraction cross times fraction numerator 7 factorial over denominator 6 factorial end fraction end cell row blank equals cell space fraction numerator 7 cross times 5 cross times 4 cross times 3 factorial over denominator 3 factorial cross times 2 end fraction end cell row blank equals cell space fraction numerator 7 cross times 5 cross times 4 over denominator 2 end fraction end cell row blank equals cell fraction numerator 140 space over denominator 2 end fraction end cell row blank equals 70 end table end style

 

ketiga-tiganya putih

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell C presubscript 5 subscript 3 space end cell row blank equals cell fraction numerator 5 factorial over denominator left parenthesis 5 minus 2 right parenthesis factorial 3 factorial end fraction end cell row blank equals cell space fraction numerator 5 factorial over denominator 2 factorial 3 factorial end fraction end cell row blank equals cell space fraction numerator 5 cross times 4 cross times 3 factorial over denominator 3 factorial cross times 2 end fraction end cell row blank equals cell space 20 over 2 end cell row blank equals 10 end table end style

Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell n left parenthesis A right parenthesis end cell equals cell 105 space plus space 70 space plus space 10 end cell row blank equals 185 end table end style

Ruang sampel :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell n left parenthesis S right parenthesis end cell equals cell C presubscript open parentheses 7 plus 5 close parentheses end presubscript subscript 3 end cell row blank equals cell C presubscript 12 subscript 3 end cell row blank equals cell fraction numerator 12 factorial over denominator open parentheses 12 minus 3 close parentheses factorial 3 factorial end fraction end cell row blank equals cell fraction numerator 12 factorial over denominator 9 factorial 3 factorial end fraction end cell row blank equals cell fraction numerator 12 cross times 11 cross times 10 cross times 9 factorial over denominator 9 factorial cross times 3 factorial end fraction end cell row blank equals 220 end table end style

sehingga, peluangnya adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis A right parenthesis end cell equals cell fraction numerator n left parenthesis A right parenthesis over denominator n left parenthesis S right parenthesis end fraction end cell row blank equals cell fraction numerator 185 over denominator 220 space end fraction end cell row blank equals cell 37 over 44 end cell row blank blank blank end table end style

Jadi, Jawaban yang tepat adalah E

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 15 Maret 2021

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved