Roboguru
SD

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

Pertanyaan

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

b. paling sedikit 3 angka.

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

 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.

Pembahasan

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.

1rb+

5.0 (2 rating)

Pertanyaan serupa

Tujuh uang logam seimbang dilantunkan. Tentukan probabilitas: a. munculnya sisi gambar tepat lima kali. b.munculnya sisi gambar sedikitnya 4 kali. c. munculnya sisi gambar paling banyak 2 kali.

325

5.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia