Contoh Soal 3 Peluang Kejadian

 $\begin{array}{ll}11.& \text{Jika kejadian}A\text{dan}B\text{adalah dua kejadian}\\ & \text{dengan}P(A)={\displaystyle \frac{8}{15},P(B)={\displaystyle \frac{7}{12},\text{dan}}}\\ & P(A|B)={\displaystyle \frac{4}{7},\text{maka nilai}P(B|A)=....}\\ & \begin{array}{l}\\ \text{a}.& {\displaystyle \frac{8}{45}}& & & \text{d}.& {\displaystyle \frac{5}{8}}\\ \\ \text{b}.& {\displaystyle \frac{1}{3}}& \text{c}.& {\displaystyle \frac{3}{8}}& \text{e}.& {\displaystyle \frac{7}{15}}\end{array}\\ \\ & \text{Jawab}:\\ & \begin{array}{rl}& \text{Kejadian di atas adalah contoh}\\ & \text{kejadian}\mathbf{\text{tidak saling bebas (bersyarat)}}.\\ & \text{Diketahui bahwa}\\ & P(A)={\displaystyle \frac{8}{15},P(B)={\displaystyle \frac{7}{12},P(A|B)={\displaystyle \frac{4}{7}}}}\\ & \text{Ditanyakan nilai}P(B|A)=...?\\ & \text{maka}\\ & \begin{array}{rl}P(A\cap B)& =P(A\cap B)\\ P(A)\times P(B|A)& =P(B)\times P(A|B)\\ P(B|A)& ={\displaystyle \frac{P(B)\times P(A|B)}{P(A)}}\\ & ={\displaystyle \frac{\left({\displaystyle \frac{7}{12}}\right)\times \left({\displaystyle \frac{4}{7}}\right)}{{\displaystyle \frac{8}{15}}}}\\ & ={\displaystyle \frac{{\displaystyle \frac{1}{3}}}{{\displaystyle \frac{8}{15}}}}\\ & ={\displaystyle \frac{1}{3}\times \frac{15}{8}}\\ & ={\displaystyle \frac{5}{8}}\end{array}\end{array}\end{array}$