Contoh Soal Distribusi Binomial (2)

$\mathbf{\text{Contoh Variabel Acak}}$

$\begin{array}{l}\\ 6.& \text{Sebuah uang logam ditos sebanyak 3 kali}\\ & \text{Jika}X\text{sebagai variabel acak dari kejadian}\\ & \text{munculnya sisi angka (A), maka peluang}\\ & \text{a. kejadian terjadi muncul 0 angka}\\ & \text{b. kejadian terjadi muncul 1 angka}\\ & \text{c. kejadian terjadi muncul 2 angka}\\ & \text{d. kejadian terjadi muncul 3 angka}\\ \\ & \mathbf{\text{Jawab}}:\\ & \text{Perhatikan bahwa}\\ & \begin{array}{rl}\text{Mula}& (1)(2)(3)\mathbf{\text{Ruang sampel}}\\ \mathbf{\text{Mulai}}& \{\begin{array}{c}A\{\begin{array}{c}A\{\begin{array}{c}A\to (A,A,A)\\ G\to (A,A,G)\end{array}\\ G\{\begin{array}{c}A\to (A,G,A)\\ G\to (A,G,G)\end{array}\end{array}\\ G\{\begin{array}{c}A\{\begin{array}{c}A\to (G,A,A)\\ G\to (G,A,G)\end{array}\\ G\{\begin{array}{c}A\to (G,G,A)\\ G\to (G,G,G)\end{array}\end{array}\end{array}\end{array}\\ & \begin{array}{rl}P(X=0)& =P((G,G,G))\\ & ={\displaystyle \frac{n(X=0)}{n(S)}}\\ & ={\displaystyle \frac{1}{8}}\\ P(X=1)& =P((G,G,A),(G,A,G),(A,G,G))\\ & ={\displaystyle \frac{n(X=1)}{n(S)}}\\ & ={\displaystyle \frac{3}{8}}\\ P(X=2)& =P((G,A,A),(A,G,A),(A,A,G))\\ & ={\displaystyle \frac{n(X=2)}{n(S)}}\\ & ={\displaystyle \frac{3}{8}}\\ P(X=3)& =P((A,A,A))\\ & ={\displaystyle \frac{n(X=3)}{n(S)}}\\ & ={\displaystyle \frac{1}{8}}\end{array}\end{array}$