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Suatu keranjang berisi bola kuning dan bola hijau. Enam bola diambil sekaligus secara acak. Peluang terambilnya bola kuning dan bola hijau adalah ...

Suatu keranjang berisi begin mathsize 14px style 6 end style bola kuning dan begin mathsize 14px style 5 end style bola hijau. Enam bola diambil sekaligus secara acak. Peluang terambilnya begin mathsize 14px style 4 end style bola kuning dan begin mathsize 14px style 2 end style bola hijau adalah ...

Jawaban:

Diketahui:

Keranjang berisi begin mathsize 14px style 6 end style bola kuning dan begin mathsize 14px style 5 end style bola hijau.

Total bola dalam keranjang begin mathsize 14px style 11 end style buah.

Enam bola diambil sekaligus secara acak.

Tentukan terlebih dahulu ruang sampelnya terambil enam bola dari begin mathsize 14px style 11 end stylebola pada kantong, yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight n open parentheses straight S close parentheses end cell equals cell straight C presubscript 6 presuperscript 11 end cell row blank equals cell fraction numerator 11 factorial over denominator open parentheses 11 minus 6 close parentheses factorial times 6 factorial end fraction end cell row blank equals cell fraction numerator 11 factorial over denominator 5 factorial times 6 factorial end fraction end cell row blank equals cell fraction numerator 11 cross times 10 cross times 9 cross times 8 cross times 7 cross times down diagonal strike 6 factorial end strike over denominator 5 cross times 4 cross times 3 cross times 2 cross times 1 cross times down diagonal strike 6 factorial end strike end fraction end cell row blank equals cell fraction numerator 55.440 over denominator 120 end fraction end cell row blank equals 462 end table end style

Kemudian tentukan titik sampelnya.

  • Terambil begin mathsize 14px style 4 end style bola dari begin mathsize 14px style 6 end style bola kuning.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight C presubscript 4 presuperscript 6 end cell equals cell fraction numerator 6 factorial over denominator left parenthesis 6 minus 4 right parenthesis factorial times 4 factorial end fraction end cell row blank equals cell fraction numerator 6 factorial over denominator 2 factorial times 4 factorial end fraction end cell row blank equals cell fraction numerator 6 cross times 5 cross times down diagonal strike 4 factorial end strike over denominator 2 cross times 1 cross times down diagonal strike 4 factorial end strike end fraction end cell row blank equals cell 30 over 2 end cell row blank equals 15 end table end style

  • Terambil begin mathsize 14px style 2 end style bola dari begin mathsize 14px style 5 end style bola hijau.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight C presubscript 2 presuperscript 5 end cell equals cell fraction numerator 5 factorial over denominator left parenthesis 5 minus 2 right parenthesis factorial times 2 factorial end fraction end cell row blank equals cell fraction numerator 5 factorial over denominator 3 factorial times 2 factorial end fraction end cell row blank equals cell fraction numerator 5 cross times 4 cross times down diagonal strike 3 factorial end strike over denominator 2 cross times 1 cross times down diagonal strike 3 factorial end strike end fraction end cell row blank equals cell 20 over 2 end cell row blank equals 10 end table end style

  • Titik sampel terambil begin mathsize 14px style 4 end style bola kuning dan begin mathsize 14px style 2 end style bola hijau.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight n open parentheses 4 straight K comma space 2 straight H close parentheses end cell equals cell straight C presubscript 4 presuperscript 6 times straight C presubscript 2 presuperscript 5 end cell row blank equals cell 15 cross times 10 end cell row blank equals 150 end table end style

Peluang terambilnya begin mathsize 14px style 4 end style bola kuning dan begin mathsize 14px style 2 end style bola hijau, yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight P open parentheses 4 straight K comma space 2 straight H close parentheses end cell equals cell fraction numerator straight n open parentheses 4 straight K comma space 2 straight H close parentheses over denominator straight n open parentheses straight S close parentheses end fraction end cell row blank equals cell 150 over 462 end cell row blank equals cell 25 over 77 end cell end table end style

Maka, Peluang terambilnya begin mathsize 14px style 4 end style bola kuning dan begin mathsize 14px style 2 end style bola hijau adalah begin mathsize 14px style 25 over 77 end style.

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