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Pertanyaan

Kotak A berisi 2 bola merah dan 3 bola putih. Kotak B berisi 5 bola hijau dan 3 bola biru. Dari masing-masing kotak diambil 2 bola sekaligus secara acak. Peluang terambilnya 2 bola putih dari kotak A dan 2 bola hijau dari kotak B adalah…

  1. 1 over 28

  2. 3 over 28

  3. 5 over 28

  4. 7 over 28

  5. 11 over 28

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Pembahasan

Peluang 2 bola putih pada kotak A = begin mathsize 12px style P left parenthesis A right parenthesis space equals space fraction numerator C left parenthesis 3 comma 2 right parenthesis over denominator C left parenthesis 5 comma 2 right parenthesis end fraction end style

begin mathsize 12px style C left parenthesis 3 comma 2 right parenthesis space equals space fraction numerator 3 factorial over denominator left parenthesis 3 minus 2 right parenthesis factorial space 2 factorial end fraction space equals fraction numerator 3 factorial over denominator 1 factorial space 2 factorial end fraction space equals space fraction numerator 3.2.1 over denominator left parenthesis 1 right parenthesis left parenthesis 2.1 right parenthesis end fraction space equals space 3 C left parenthesis 5 comma 2 right parenthesis space equals space fraction numerator 5 factorial over denominator left parenthesis 5 minus 2 right parenthesis factorial space 2 factorial end fraction space equals fraction numerator 5 factorial over denominator 3 factorial space 2 factorial end fraction space equals space fraction numerator 5.4.3.2.1 over denominator left parenthesis 3.2.1 right parenthesis left parenthesis 2.1 right parenthesis end fraction space equals space 10 P left parenthesis A right parenthesis space equals space 3 over 10 end style

Peluang 2 bola hijau pada kotak B =

begin mathsize 12px style P left parenthesis B right parenthesis equals fraction numerator C left parenthesis 5 comma 2 right parenthesis over denominator C left parenthesis 8 comma 2 right parenthesis end fraction end style

begin mathsize 12px style C left parenthesis 5 comma 2 right parenthesis space equals space fraction numerator 5 factorial over denominator left parenthesis 5 minus 2 right parenthesis factorial space 2 factorial end fraction space equals space fraction numerator 5 factorial over denominator 3 factorial space 2 factorial end fraction space equals space fraction numerator 5.4.3.2.1 over denominator left parenthesis 3.2.1 right parenthesis left parenthesis 2.1 right parenthesis end fraction space equals space 10 C left parenthesis 8 comma 2 right parenthesis space equals space fraction numerator 8 factorial over denominator left parenthesis 8 minus 2 right parenthesis factorial space 2 factorial end fraction space equals space fraction numerator 8 factorial over denominator 6 factorial space 2 factorial end fraction space equals space fraction numerator 8.7.6.5.4.3.2.1 over denominator left parenthesis 6.5.4.3.2.1 right parenthesis left parenthesis 2.1 right parenthesis end fraction space equals space 28 P left parenthesis B right parenthesis space equals space 10 over 28 end style

Peluang terambilnya 2 bola putih dari kotak A dan 2 bola hijau dari kotak B adalah

begin mathsize 12px style 3 over 10.10 over 28 equals 3 over 28 end style

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