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Sebanyak 12 kartu diberi nomor 1 sampai 12, kartu ...

Sebanyak 12 kartu diberi nomor 1 sampai 12, kartu tersebut dikocok kemudian diambil dua kartu secara acak. Peluang terambil 2 kartu kelipatan 3 adalah ...undefined

  1. begin mathsize 14px style 1 fourth end style

  2. begin mathsize 14px style 2 over 11 end style

  3. begin mathsize 14px style 1 over 6 end style

  4. begin mathsize 14px style 1 over 11 end style

  5. begin mathsize 14px style 1 over 22 end style

Jawaban:

Perhatikan perhitungan berikut.

Ingat, kombinasi:

begin mathsize 14px style straight C subscript r superscript n equals fraction numerator n factorial over denominator r factorial times open parentheses n minus r close parentheses factorial end fraction end style

Maka:

Kartu kelipatan 3 adalah begin mathsize 14px style open curly brackets 3 comma space 6 comma space 9 comma space 12 close curly brackets equals 4 end style.

Peluang terambil 2 kartu kelipatan 3 yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight P equals cell fraction numerator straight C subscript 2 superscript 4 over denominator straight C subscript 2 superscript 12 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 4 factorial over denominator 2 factorial times 2 factorial end fraction end style over denominator begin display style fraction numerator 12 factorial over denominator 2 factorial times 10 factorial end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 4 times 3 times 2 factorial over denominator 2 factorial times 2 factorial end fraction end style over denominator begin display style fraction numerator 12 times 11 times 10 factorial over denominator 2 factorial times 10 factorial end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 4 times 3 over denominator 2 factorial end fraction end style over denominator begin display style fraction numerator 12 times 11 over denominator 2 factorial end fraction end style end fraction end cell row blank equals cell fraction numerator 12 over denominator 12 times 11 end fraction end cell row blank equals cell 1 over 11 end cell end table end style

Jadi, peluang terambilnya 2 kartu kelipatan 3 adalah begin mathsize 14px style 1 over 11 end style.

Dengan demikian, jawaban yang tepat adalah D.

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