Question

A and B are two independent events. The probability that both A and B occur is $\frac{1}{6}$ and the probability that neither of them occurs is $\frac{1}{3}$. The probability of occurrence of A is?

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{5}{6}$
• D. $\frac{1}{6}$

Answer 1

Answer: (B)

$\frac{1}{3}$

$\begin{array}{c}P\left(A\cap C\right)=\frac{1}{6}\\ P\left(\overline{A}\cap \overline{C}\right)=\frac{1}{3}\\ P\left(A\right)=?\\ ifeventsisindependentthen\\ P\left(A\cap C\right)=P\left(A\right)\times P\left(B\right)\\ \frac{1}{6}=P\left(A\right)\times P\left(B\right)....\left(1\right)\\ P\left(\overline{A}\cap \overline{C}\right)=P\left(\overline{A}\right)\times P\left(\overline{B}\right)=\frac{1}{3}\end{array}$