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Kepala bagian produksi PT sejahtera melaporkan bahwa rata-rata produksi TV yang rusak setiap kali produksi sebesar 15%. dari total produksi tersebut diambil secara acak sebanyak 6 unit TV. Tentukan peluang: a. paling banyak 1 TV rusak b. paling banyak 2 TV rusak

Pertanyaan

Kepala bagian produksi PT sejahtera melaporkan bahwa rata-rata produksi TV yang rusak setiap kali produksi sebesar 15 percent sign. dari total produksi tersebut diambil secara acak sebanyak 6 unit TV. Tentukan peluang:

a. paling banyak 1 TV rusak
b. paling banyak 2 TV rusak

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

peluang paling banyak 2 TV rusak adalah 0 comma 889

Pembahasan

Ingat!

Rumus distribusi binomial kumulatif yaitu

f open parentheses t close parentheses equals begin inline style sum from x equals 0 to t of end style straight C open parentheses n comma space x close parentheses times p to the power of x times q to the power of n minus x end exponent 

Dengan : 

x equals banyak kejadian yang diharapkan 
p equals peluang kejadian yang diharapkan 
q equals peluang kejadian yang tidak diharapkan open parentheses q equals 1 minus p close parentheses  
n equals banyaknya semua kejadian

Perhatikan perhitungan berikut!

Dari soal tersebut diketahui 

table attributes columnalign right center left columnspacing 0px end attributes row p equals cell 15 percent sign equals 0 comma 15 end cell row q equals cell 1 minus 0 comma 15 equals 0 comma 85 end cell row n equals 6 end table 

Maka 

Untuk x equals 0  

table attributes columnalign right center left columnspacing 0px end attributes row cell straight P open parentheses 0 close parentheses end cell equals cell straight C open parentheses 6 comma space 0 close parentheses times open parentheses 0 comma 15 close parentheses to the power of 0 times open parentheses 0 comma 85 close parentheses to the power of 6 minus 0 end exponent end cell row blank equals cell fraction numerator 6 factorial over denominator open parentheses 6 minus 0 close parentheses factorial times 0 factorial end fraction times open parentheses 0 comma 15 close parentheses to the power of 0 times open parentheses 0 comma 85 close parentheses to the power of 6 end cell row blank equals cell fraction numerator 6 factorial over denominator 6 factorial times 1 end fraction times 1 times 0 comma 377 end cell row blank equals cell 1 times 1 times 0 comma 377 end cell row blank equals cell 0 comma 377 end cell end table 

Untuk x equals 1 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight P open parentheses 1 close parentheses end cell equals cell straight C open parentheses 6 comma space 1 close parentheses times open parentheses 0 comma 15 close parentheses to the power of 1 times open parentheses 0 comma 85 close parentheses to the power of 6 minus 1 end exponent end cell row blank equals cell fraction numerator 6 factorial over denominator open parentheses 6 minus 1 close parentheses factorial times 1 factorial end fraction times open parentheses 0 comma 15 close parentheses to the power of 1 times open parentheses 0 comma 85 close parentheses to the power of 5 end cell row blank equals cell fraction numerator 6 factorial over denominator 5 factorial times 1 factorial end fraction times 0 comma 15 times 0 comma 444 end cell row blank equals cell fraction numerator 6 times 5 factorial over denominator 5 factorial times 1 factorial end fraction times 0 comma 15 times 0 comma 444 end cell row blank equals cell 6 times 0 comma 15 times 0 comma 444 end cell row blank equals cell 0 comma 340 end cell end table 

Untuk x equals 2 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight P open parentheses 2 close parentheses end cell equals cell straight C open parentheses 6 comma space 2 close parentheses times open parentheses 0 comma 15 close parentheses squared times open parentheses 0 comma 85 close parentheses to the power of 6 minus 2 end exponent end cell row blank equals cell fraction numerator 6 factorial over denominator open parentheses 6 minus 2 close parentheses factorial times 2 factorial end fraction times open parentheses 0 comma 15 close parentheses squared times open parentheses 0 comma 85 close parentheses to the power of 4 end cell row blank equals cell fraction numerator 6 factorial over denominator 4 factorial times 2 factorial end fraction times 0 comma 022 times 0 comma 522 end cell row blank equals cell fraction numerator 6 times 5 times 4 factorial over denominator 4 factorial times 2 times 1 end fraction times 0 comma 022 times 0 comma 522 end cell row blank equals cell 15 times 0 comma 022 times 0 comma 522 end cell row blank equals cell 0 comma 172 end cell end table 

a. Peluang paling banyak 1 TV rusak open parentheses t equals 1 close parentheses yaitu 

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 1 close parentheses end cell equals cell begin inline style sum from x equals 0 to 1 of end style straight C open parentheses n comma space x close parentheses times p to the power of x times q to the power of n minus x end exponent end cell row blank equals cell straight P open parentheses 0 close parentheses plus straight P open parentheses 1 close parentheses end cell row blank equals cell 0 comma 377 plus 0 comma 340 end cell row blank equals cell 0 comma 717 end cell end table  

Jadi, peluang paling banyak 1 TV rusak adalah 0 comma 717

b. Peluang paling banyak 2 TV rusak open parentheses t equals 2 close parentheses yaitu 

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 2 close parentheses end cell equals cell begin inline style sum from x equals 0 to 2 of end style straight C open parentheses n comma space x close parentheses times p to the power of x times q to the power of n minus x end exponent end cell row blank equals cell straight P open parentheses 0 close parentheses plus straight P open parentheses 1 close parentheses plus straight P open parentheses 2 close parentheses end cell row blank equals cell 0 comma 377 plus 0 comma 340 plus 0 comma 172 end cell row blank equals cell 0 comma 889 end cell end table 

Jadi, peluang paling banyak 2 TV rusak adalah 0 comma 889

9rb+

4.5 (22 rating)

Indra Kurniawan

Makasih ❤️

Della Fitri

Jawaban tidak sesuai

Pertanyaan serupa

Sebuah koin dilantunkan sebanyak 8 kali. Tentukan probabilitas: tepat muncul 3 sisi gambar. paling sedikit muncul 3 sisi gambar.

1rb+

4.5

Jawaban terverifikasi

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