Question

A and B are two independent events such that $P(A^{\prime }\cap B^{\prime })=\frac{1}{6}$ and $P\left(A^{\prime }\right)=\frac{5}{24}$. Then P(B) is equal to

• A. $\frac{4}{5}$
• B. $\frac{1}{6}$
• C. $\frac{1}{5}$
• D. $\frac{5}{6}$

Answer 1

Answer: (C)

$\frac{1}{5}$

Given: A and B are two independent events and

$P(\overline{A}\bigcap \overline{B})=\frac{1}{6},P\left(\overline{A}\right)=\frac{5}{24}$

$\therefore$ Using

$P(\overline{A}\bigcap \overline{B})=P\left(\overline{A}\right)P\left(\overline{B}\right)$

$\frac{1}{6}=\frac{5}{24}P\left(\overline{B}\right)$

i.e., $P\left(\overline{B}\right)=\frac{4}{5}$ then

$P\left(B\right)=1-P\left(\overline{B}\right)=1-\frac{4}{5}=\frac{1}{5}$