Question

If $A$ and $B$ are two independent events. The probability that both $A$ and $B$ occurs is $\frac{1}{12}$ and probability neither $A$ nor $B$ occurs is $\frac{1}{2}$, then

• A. $P(A) = \frac{1}{3}, P(B) = 1/4$
• B. $P(A) = \frac{1}{2}, P(B) = 1/6$
• C. $ P(A) = 1/6, P(B) = 1/2$
• D. $P(A) = \frac{1}{4}, P(B) = 1/3$

Answer 1

Answer: (A), (D)

Given, $P(AB) = P(A) P(B) = \frac{1}{12}\,....(1)$
$P(\overline{AB}) = P(\bar{A})P(\bar{B}) = 1/2$
$=[ 1 - P(A)] [1 - P(B)] = 1/2\,....(ii)$
Only options (a) and (d) satisfies both (i) and (ii).