If A and B are two independent events. The probability that both A and B occurs is (1/12) and probability neither A nor B occurs is (1/2), then

Question

If A and B are two independent events. The probability that both A and B occurs is (1/12) and probability neither A nor B occurs is (1/2), then (A) P(A) = (1/3), P(B) = 1/4 (B) P(A) = (1/2), P(B) = 1/6 (C)  P(A) = 1/6, P(B) = 1/2 (D) P(A) = (1/4), P(B) = 1/3

Tardigrade Admin · Accepted Answer

Given, P(AB) = P(A) P(B) = (1/12) ....(1) P( overlineAB) = P( barA)P( barB) = 1/2 =[ 1 - P(A)] [1 - P(B)] = 1/2 ....(ii) Only options (a) and (d) satisfies both (i) and (ii).

Q. 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

$P (A) = \frac{1}{3}, P (B) = 1/4$

$P (A) = \frac{1}{2}, P (B) = 1/6$

$P (A) = 1/6, P (B) = 1/2$

$P (A) = \frac{1}{4}, P (B) = 1/3$

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

Q. If A and B are two independent events. The probability that both A and B occurs is 121​ and probability neither A nor B occurs is 21​, then

P(A)=31​,P(B)=1/4

P(A)=21​,P(B)=1/6

P(A)=1/6,P(B)=1/2

P(A)=41​,P(B)=1/3