Sebuah dadu dilambungkan sebanyak 5 kali. Peluang muncul mata dadu genap paling banyak tiga kali sebesar ...

Pertanyaan

Sebuah dadu dilambungkan sebanyak 5 kali. Peluang muncul mata dadu genap paling banyak tiga kali sebesar ...

  1. begin mathsize 14px style 5 over 32 end style 

  2. begin mathsize 14px style 3 over 16 end style 

  3. begin mathsize 14px style 1 fourth end style 

  4. begin mathsize 14px style 15 over 32 end style 

  5. begin mathsize 14px style 13 over 16 end style 

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

peluang muncul dadu genap paling banyak 3 kali adalah begin mathsize 14px style 25 over 32 end style.

Pembahasan

Sebuah dadu dilempar sebanyak 5 kali,
muncul dadu genap paling banyak 3 kali, begin mathsize 14px style straight r equals 1 space atau space straight r equals 2 space atau space straight r equals 3 end style.
Angka genap dalam mata dadu adalah begin mathsize 14px style left curly bracket 2 comma space 4 comma space 6 right curly bracket end style.

Peluang muncul angka genap:

begin mathsize 14px style straight p equals 3 over 6 equals 1 half end style 

Peluang muncul angka ganjil:

begin mathsize 14px style straight q equals 3 over 6 equals 1 half end style 

Peluang muncul dadu genap 1 kali begin mathsize 14px style left parenthesis straight r equals 1 right parenthesis end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight P equals cell straight C subscript straight r superscript straight n cross times straight p to the power of straight r cross times straight q to the power of straight n minus straight r end exponent end cell row blank equals cell straight C subscript 1 superscript 5 cross times open parentheses 1 half close parentheses to the power of 1 cross times open parentheses 1 half close parentheses to the power of 5 minus 1 end exponent end cell row blank equals cell fraction numerator 5 factorial over denominator left parenthesis 5 minus 1 right parenthesis factorial 1 factorial end fraction cross times open parentheses 1 half close parentheses to the power of 1 cross times open parentheses 1 half close parentheses to the power of 5 minus 1 end exponent end cell row blank equals cell fraction numerator 5 over denominator 1 factorial end fraction cross times 1 over 32 end cell row blank equals cell 5 over 32 end cell end table end style 

Peluang muncul dadu genap 2 kali begin mathsize 14px style left parenthesis straight r equals 2 right parenthesis end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight P equals cell straight C subscript straight r superscript straight n cross times straight p to the power of straight r cross times straight q to the power of straight n minus straight r end exponent end cell row blank equals cell straight C subscript 2 superscript 5 cross times open parentheses 1 half close parentheses squared cross times open parentheses 1 half close parentheses to the power of 5 minus 2 end exponent end cell row blank equals cell fraction numerator 5 factorial over denominator left parenthesis 5 minus 2 right parenthesis factorial 2 factorial end fraction cross times open parentheses 1 half close parentheses squared cross times open parentheses 1 half close parentheses to the power of 5 minus 2 end exponent end cell row blank equals cell fraction numerator 5 over denominator 2 factorial end fraction cross times 1 over 8 end cell row blank equals cell 5 over 16 end cell end table end style 

Peluang muncul dadu genap 3 kali begin mathsize 14px style left parenthesis straight r equals 3 right parenthesis end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight P equals cell straight C subscript straight r superscript straight n cross times straight p to the power of straight r cross times straight q to the power of straight n minus straight r end exponent end cell row blank equals cell straight C subscript 3 superscript 5 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 to the power of 5 minus 3 end exponent end cell row blank equals cell fraction numerator 5 over denominator 2 factorial end fraction cross times 1 over 8 end cell row blank equals cell 5 over 16 end cell end table end style 

Peluang muncul dadu genap paling banyak 3 kali:

begin mathsize 14px style 5 over 32 plus 5 over 16 plus 5 over 16 equals 25 over 32 end style 

Jadi, peluang muncul dadu genap paling banyak 3 kali adalah begin mathsize 14px style 25 over 32 end style.

Pertanyaan serupa

Tiga mata uang logam dilempar secara bersamaan sebanyak 400 kali. Tentukan frekuensi harapan muncul tepat dua gambar satu angka?

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