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Sebuah kotak berisi 30 bola. Sebanyak 18 bola berwarna merah dan hijau. Dari kotak diambil 8 bola secara acak. Peluang terambil paling banyak 5 bola hijau adalah ...

Sebuah kotak berisi  bola. Sebanyak  bola berwarna merah dan hijau. Dari kotak diambil  bola secara acak. Peluang terambil paling banyak  bola hijau adalah ...

  1. begin mathsize 14px style 0 comma 8125 end style 

  2. begin mathsize 14px style 0 comma 9502 end style 

  3. begin mathsize 14px style 0 comma 1239 end style 

  4. begin mathsize 14px style 0 comma 6177 end style 

  5. begin mathsize 14px style 0 comma 3125 end style 

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S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban tidak ada yang tepat.

jawaban tidak ada yang tepat.

Pembahasan

Diketahui: Kotak berisi bola Bola merah dan bola hijau Terambil paling banyak bola hijau dari bola, maka: bola hijau dan bola merah bola hijau dan bola merah bola hijau dan bola merah bola hijau Diperoleh bola dengan bola hijau Sehingga didapat peluang Peluang terambil paling banyak bola hijau adalah . Jadi, jawaban tidak ada yang tepat.

Diketahui:

Kotak berisi begin mathsize 14px style 30 end style bola

Bola merah begin mathsize 14px style 18 end style dan bola hijau begin mathsize 14px style 12 end style

Terambil paling banyak begin mathsize 14px style 5 end style bola hijau dari begin mathsize 14px style 8 end style bola, maka:

begin mathsize 14px style 5 end style bola hijau dan undefined bola merah

begin mathsize 12px style table attributes columnalign center center left end attributes row cell scriptbase C subscript 5 times end scriptbase presubscript 12 scriptbase C subscript 3 times end scriptbase presubscript 18 end cell equals cell fraction numerator 12 factorial over denominator open parentheses 12 minus 5 close parentheses factorial times 5 factorial end fraction times fraction numerator 18 factorial over denominator open parentheses 18 minus 3 close parentheses factorial times 3 factorial end fraction end cell row space equals cell fraction numerator 12 factorial over denominator 7 factorial times 5 factorial end fraction times fraction numerator 18 factorial over denominator 15 factorial times 3 factorial end fraction end cell row space equals cell fraction numerator 12 cross times 11 cross times 10 cross times 9 cross times 8 cross times down diagonal strike 7 factorial end strike over denominator down diagonal strike 7 factorial end strike times 5 cross times 4 cross times 3 cross times 2 cross times 1 end fraction times fraction numerator 18 cross times 17 cross times 16 cross times down diagonal strike 15 factorial end strike over denominator down diagonal strike 15 factorial end strike times 3 cross times 2 cross times 1 end fraction end cell row space equals cell 95040 over 120 times 4896 over 6 end cell row space equals cell 465315840 over 720 end cell row space equals cell 646.272 end cell end table end style

undefined bola hijau dan undefined bola merah

begin mathsize 12px style table attributes columnalign center center left end attributes row cell scriptbase C subscript 6 times end scriptbase presubscript 12 scriptbase C subscript 2 times end scriptbase presubscript 18 end cell equals cell fraction numerator 12 factorial over denominator left parenthesis 12 minus 6 right parenthesis factorial times 6 factorial end fraction times fraction numerator 18 factorial over denominator left parenthesis 18 minus 2 right parenthesis factorial times 2 factorial end fraction end cell row space equals cell fraction numerator 12 factorial over denominator 6 factorial times 6 factorial end fraction times fraction numerator 18 factorial over denominator 16 factorial times 2 factorial end fraction end cell row space equals cell fraction numerator 12 cross times 11 cross times 10 cross times 9 cross times 8 cross times 7 cross times down diagonal strike 6 factorial end strike over denominator down diagonal strike 6 factorial end strike times 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 end fraction times fraction numerator 18 cross times 17 cross times down diagonal strike 16 factorial end strike over denominator down diagonal strike 16 factorial end strike times 2 cross times 1 end fraction end cell row space equals cell 665280 over 720 times 306 over 2 end cell row space equals cell 203575680 over 1440 end cell row space equals cell 141.372 end cell end table end style

undefined bola hijau dan undefined bola merah

begin mathsize 14px style table attributes columnalign center center left end attributes row cell scriptbase C subscript 7 times end scriptbase presubscript 12 scriptbase C subscript 1 times end scriptbase presubscript 18 end cell equals cell fraction numerator 12 factorial over denominator left parenthesis 12 minus 7 right parenthesis factorial times 7 factorial end fraction times fraction numerator 18 factorial over denominator left parenthesis 18 minus 1 right parenthesis factorial times 1 factorial end fraction end cell row space equals cell fraction numerator 12 factorial over denominator 5 factorial times 7 factorial end fraction times fraction numerator 18 factorial over denominator 17 factorial times 1 factorial end fraction end cell row space equals cell fraction numerator 12 cross times 11 cross times 10 cross times 9 cross times 8 cross times down diagonal strike 7 factorial end strike over denominator 5 cross times 4 cross times 3 cross times 2 cross times 1 times down diagonal strike 7 factorial end strike end fraction times fraction numerator 18 cross times down diagonal strike 17 factorial end strike over denominator down diagonal strike 17 factorial end strike times 1 end fraction end cell row space equals cell 95040 over 120 cross times 18 end cell row space equals cell 792 cross times 18 end cell row space equals cell 14.256 end cell end table end style

begin mathsize 14px style 8 end style bola hijau 

begin mathsize 14px style table attributes columnalign center center left end attributes row cell scriptbase C subscript 8 end scriptbase presubscript 12 end cell equals cell fraction numerator 12 factorial over denominator left parenthesis 12 minus 8 right parenthesis factorial times 8 factorial end fraction end cell row space equals cell fraction numerator 12 factorial over denominator 4 factorial times 8 factorial end fraction end cell row space equals cell fraction numerator 12 cross times 11 cross times 10 cross times 9 cross times down diagonal strike 8 factorial end strike over denominator 4 cross times 3 cross times 2 cross times 1 times down diagonal strike 8 factorial end strike end fraction end cell row space equals cell 11880 over 24 end cell row space equals 495 row space space space end table end style

Diperoleh begin mathsize 14px style n left parenthesis A right parenthesis equals 646.272 plus 141.372 plus 14.256 plus 495 equals 802.395 end style   

begin mathsize 14px style 30 end style bola dengan bola hijau begin mathsize 14px style 12 end style

begin mathsize 14px style table attributes columnalign center center left end attributes row cell scriptbase C subscript 12 end scriptbase presubscript 30 end cell equals cell fraction numerator 30 factorial over denominator open parentheses 30 minus 12 close parentheses factorial times 12 factorial end fraction end cell row space equals cell fraction numerator 30 factorial over denominator 18 factorial times 12 factorial end fraction end cell row space equals cell 86.493.225 end cell end table end style

Sehingga didapat peluang

begin mathsize 14px style table attributes columnalign center center left end attributes row cell P open parentheses A close parentheses end cell equals cell fraction numerator n open parentheses A close parentheses over denominator n open parentheses S close parentheses end fraction end cell row space equals cell fraction numerator 802.395 over denominator 86.493.225 end fraction end cell row space equals cell 0 comma 00927697 end cell end table end style

Peluang terambil paling banyak begin mathsize 14px style 5 end style bola hijau adalah begin mathsize 14px style 0 comma 00927697 end style.

Jadi, jawaban tidak ada yang tepat.

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