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Peluang bahwa seseorang yang melemparkan  mata uan...

Peluang bahwa seseorang yang melemparkan begin mathsize 14px style 3 end style mata uang logam sekaligus akan menghasilkan semuanya angka atau semuanya gambar untuk kedua kalinya pada pelemparan kelima adalah ....

Jawaban:

Dari soal dapat diketahui:

begin mathsize 14px style straight n equals 5 comma space straight x equals 2 comma space straight p equals 1 over 8 comma space straight q equals 7 over 8 end style 

Dimisalkan:

begin mathsize 14px style straight A equals kejadian space muncul space semuanya space angka straight B equals kejadian space muncul space semuanya space gambar end style 

Maka:

- Menentukan peluang kejadian A

begin mathsize 14px style straight P open parentheses straight X equals straight x close parentheses equals straight C subscript straight x superscript straight n times straight p to the power of straight x times straight q to the power of straight n minus straight x end exponent straight P open parentheses straight A equals 2 close parentheses equals straight C subscript 2 superscript 5 times open parentheses 1 over 8 close parentheses squared times open parentheses 7 over 8 close parentheses to the power of 5 minus 2 end exponent straight P open parentheses straight A equals 2 close parentheses equals fraction numerator 5 factorial over denominator 3 factorial times 2 factorial end fraction times 1 over 64 times open parentheses 7 over 8 close parentheses cubed straight P open parentheses straight A equals 2 close parentheses equals fraction numerator 5 times 4 times 3 factorial over denominator 3 factorial times 2 times 1 end fraction times 1 over 64 times 343 over 512 straight P open parentheses straight A equals 2 close parentheses equals 10 times 1 over 64 times 343 over 512 straight P open parentheses straight A equals 2 close parentheses equals 5 times 1 over 32 times 343 over 512 straight P open parentheses straight A equals 2 close parentheses equals fraction numerator 1.715 over denominator 16384 end fraction end style 

- Menentukan peluang kejadian B

begin mathsize 14px style straight P open parentheses straight X equals straight x close parentheses equals straight C subscript straight x superscript straight n times straight p to the power of straight x times straight q to the power of straight n minus straight x end exponent straight P open parentheses straight B equals 2 close parentheses equals straight C subscript 2 superscript 5 times open parentheses 1 over 8 close parentheses squared times open parentheses 7 over 8 close parentheses to the power of 5 minus 2 end exponent straight P open parentheses straight B equals 2 close parentheses equals fraction numerator 5 factorial over denominator 3 factorial times 2 factorial end fraction times 1 over 64 times open parentheses 7 over 8 close parentheses cubed straight P open parentheses straight B equals 2 close parentheses equals fraction numerator 5 times 4 times 3 factorial over denominator 3 factorial times 2 times 1 end fraction times 1 over 64 times 343 over 512 straight P open parentheses straight B equals 2 close parentheses equals 10 times 1 over 64 times 343 over 512 straight P open parentheses straight B equals 2 close parentheses equals 5 times 1 over 32 times 343 over 512 straight P open parentheses straight B equals 2 close parentheses equals fraction numerator 1.715 over denominator 16384 end fraction end style 

Sehingga:

begin mathsize 14px style straight P open parentheses straight A close parentheses space atau space straight P open parentheses straight B close parentheses equals straight P open parentheses straight A close parentheses plus straight P open parentheses straight B close parentheses straight P open parentheses straight A close parentheses space atau space straight P open parentheses straight B close parentheses equals fraction numerator 1.715 over denominator 16.384 end fraction plus fraction numerator 1.715 over denominator 16.384 end fraction straight P open parentheses straight A close parentheses space atau space straight P open parentheses straight B close parentheses equals fraction numerator 3.430 over denominator 16.384 end fraction straight P open parentheses straight A close parentheses space atau space straight P open parentheses straight B close parentheses equals fraction numerator 1.715 over denominator 8.192 end fraction end style 

Jadi, peluang menghasilkan semuanya angka atau semuanya gambar untuk kedua kalinya pada pelemparan kelima adalah begin mathsize 14px style fraction numerator 1.715 over denominator 8.192 end fraction end style.

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