Sepuluh uang logam yang sisinya gambar dan angka dilambungkan secara bersama-sama. Peluang munculnya tepat enam sisi angka adalah ...

Pertanyaan

$begin mathsize 14px style fraction numerator 104 over denominator 1.105 end fraction end style$
$begin mathsize 14px style fraction numerator 105 over denominator 1.105 end fraction end style$
$begin mathsize 14px style fraction numerator 106 over denominator 1.105 end fraction end style$
$begin mathsize 14px style fraction numerator 105 over denominator 1.024 end fraction end style$
$fraction numerator size 14px 106 over denominator size 14px 1 size 14px. size 14px 024 end fraction$

Pembahasan Soal:

Peluang muncul gambar $begin mathsize 14px style p equals 1 half end style$

Peluang muncul angka $begin mathsize 14px style q equals 1 minus p equals 1 minus 1 half equals 1 half end style$

Tepat enam sisi angka dari 10 uang logam yang dilempar

$begin mathsize 14px style n equals 10 end style$
muncul sisi angka $begin mathsize 14px style r equals 6 end style$
muncul sisi gambar $begin mathsize 14px style n minus r equals 10 minus 6 equals 4 end style$
Peluang tepat enam sisi angka dari sepuluh uang logam yang dilempar

$begin mathsize 14px style C presubscript n subscript r cross times space p to the power of r space cross times q to the power of n minus r end exponent equals C presubscript 10 subscript 6 cross times open parentheses 1 half close parentheses to the power of 6 cross times open parentheses 1 half close parentheses to the power of 4 space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 10 factorial over denominator left parenthesis 10 minus 6 right parenthesis factorial 6 factorial end fraction cross times 1 over 64 cross times 1 over 16 space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 10 cross times 9 cross times 8 cross times 7 over denominator 4 cross times 3 cross times 2 cross times 1 end fraction cross times 1 over 1024 space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 210 cross times 1 over 1024 space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 105 over 512 end style$

Jadi, jawaban yang tepat adalah B

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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