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Sekeping uang logam dilemparkan sebanyak 5 kali, hitunglah probabilitas memperoleh: b. paling sedikit 3 angka.

Sekeping uang logam dilemparkan sebanyak 5 kali, hitunglah probabilitas memperoleh:

b. paling sedikit 3 angka.

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A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

probabilitas memperoleh paling sedikit 3angka yaitu .

 probabilitas memperoleh paling sedikit 3 angka yaitu begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 71 over 192 end cell end table end style.

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Pembahasan

Dengan menggunakan distribusi binomial, maka didapat: Jadi,probabilitas memperoleh paling sedikit 3angka yaitu .

Dengan menggunakan distribusi binomial, maka didapat:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row p equals cell peluang space muncul space angka end cell row blank equals cell 1 half end cell row q equals cell peluang space muncul space bukan space angka end cell row blank equals cell 1 minus p end cell row blank equals cell 1 minus 1 half end cell row blank equals cell 1 half end cell row blank blank blank row cell P left parenthesis 3 right parenthesis end cell equals cell C presubscript n subscript r cross times p to the power of r cross times q to the power of n minus r end exponent end cell row blank equals cell C presubscript 5 subscript 3 cross times open parentheses 1 half close parentheses cubed cross times open parentheses 1 half close parentheses to the power of 5 minus 3 end exponent end cell row blank equals cell fraction numerator 5 factorial over denominator left parenthesis 5 minus 3 right parenthesis factorial 3 factorial end fraction cross times open parentheses 1 half close parentheses cubed cross times open parentheses 1 half close parentheses squared end cell row blank equals cell fraction numerator 5 cross times 4 cross times 3 factorial over denominator 2 cross times 1 cross times 3 factorial end fraction cross times 1 over 8 cross times 1 fourth end cell row blank equals cell 10 cross times 1 over 32 end cell row blank equals cell 5 over 16 end cell row blank blank blank row cell P open parentheses 4 close parentheses end cell equals cell C presubscript n subscript r cross times p to the power of r cross times q to the power of n minus r end exponent end cell row blank equals cell C presubscript 5 subscript 4 cross times open parentheses 1 half close parentheses to the power of 4 cross times open parentheses 1 half close parentheses to the power of 5 minus 4 end exponent end cell row blank equals cell fraction numerator 5 factorial over denominator left parenthesis 5 minus 4 right parenthesis factorial 4 factorial end fraction cross times open parentheses 1 half close parentheses to the power of 4 cross times open parentheses 1 half close parentheses to the power of 1 end cell row blank equals cell fraction numerator 5 cross times 4 factorial over denominator 3 cross times 2 cross times 1 cross times 4 factorial end fraction cross times 1 over 16 cross times 1 half end cell row blank equals cell 5 over 6 cross times 1 over 32 end cell row blank equals cell 5 over 192 end cell row blank blank blank row cell P open parentheses 5 close parentheses end cell equals cell C presubscript n subscript r cross times p to the power of r cross times q to the power of n minus r end exponent end cell row blank equals cell C presubscript 5 subscript 5 cross times open parentheses 1 half close parentheses to the power of 5 cross times open parentheses 1 half close parentheses to the power of 5 minus 5 end exponent end cell row blank equals cell fraction numerator 5 factorial over denominator left parenthesis 5 minus 5 right parenthesis factorial 5 factorial end fraction cross times open parentheses 1 half close parentheses to the power of 5 cross times open parentheses 1 half close parentheses to the power of 0 end cell row blank equals cell fraction numerator 5 factorial over denominator 0 factorial 5 factorial end fraction cross times 1 over 32 cross times 1 end cell row blank equals cell 1 cross times 1 over 32 end cell row blank equals cell 1 over 32 end cell row blank blank blank row Peluang equals cell 5 over 16 plus 5 over 192 plus 1 over 32 end cell row blank equals cell fraction numerator 60 plus 5 plus 6 over denominator 192 end fraction end cell row blank equals cell 71 over 192 end cell end table end style

Jadi, probabilitas memperoleh paling sedikit 3 angka yaitu begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 71 over 192 end cell end table end style.

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