Contoh Soal Distribusi Binomial (2)

$\color{blue}\textbf{Contoh Variabel Acak}$

$\begin{array}{ll}\\ 6.&\textrm{Sebuah uang logam ditos sebanyak 3 kali}\\ &\textrm{Jika}\: \: X\: \: \textrm{sebagai variabel acak dari kejadian}\\ &\textrm{munculnya sisi angka (A), maka peluang}\\ &\textrm{a. kejadian terjadi muncul 0 angka}\\ &\textrm{b. kejadian terjadi muncul 1 angka}\\ &\textrm{c. kejadian terjadi muncul 2 angka}\\ &\textrm{d. kejadian terjadi muncul 3 angka}\\\\ &\color{blue}\textbf{Jawab}:\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned} \color{blue}\textrm{Mula}\: \, &\color{red}(1)\quad (2)\quad (3)\quad \color{blue}\textbf{Ruang sampel}\\ \textbf{Mulai}&\left\{\begin{matrix} A\left\{\begin{matrix} A\left\{\begin{matrix} A\rightarrow (A,A,A)\\ G\rightarrow (A,A,G) \end{matrix}\right.\\ G\left\{\begin{matrix} A\rightarrow (A,G,A)\\ G\rightarrow (A,G,G) \end{matrix}\right. \end{matrix}\right.\\ G\left\{\begin{matrix} A\left\{\begin{matrix} A\rightarrow (G,A,A)\\ G\rightarrow (G,A,G) \end{matrix}\right.\\ G\left\{\begin{matrix} A\rightarrow (G,G,A)\\ G\rightarrow (G,G,G) \end{matrix}\right. \end{matrix}\right. \end{matrix}\right. \end{aligned}\\ &\begin{aligned}P(X=0)&=P((G,G,G))\\ &=\displaystyle \frac{n(X=0)}{n(S)}\\ &=\color{red}\displaystyle \frac{1}{8}\\ P(X=1)&=P((G,G,A),(G,A,G),(A,G,G))\\ &=\displaystyle \frac{n(X=1)}{n(S)}\\ &=\color{red}\displaystyle \frac{3}{8}\\ P(X=2)&=P((G,A,A),(A,G,A),(A,A,G))\\ &=\displaystyle \frac{n(X=2)}{n(S)}\\ &=\color{red}\displaystyle \frac{3}{8}\\ P(X=3)&=P((A,A,A))\\ &=\displaystyle \frac{n(X=3)}{n(S)}\\ &=\color{red}\displaystyle \frac{1}{8} \end{aligned} \end{array}$