Box $A$ contains 2 block and 3 red balls while box $B$ contains 3 black and 4 red balls. Out of thes

Question

Box $A$ contains 2 block and 3 red balls while box $B$ contains 3 black and 4 red balls. Out of these two boxes one is selected at random and the probability of choosing box $A$ is double that of box $B$. If a red ball is drawn from the selected box, then the probability that it has come from box $B$ is:

Professor PC Thomas Classes · Answer

$\begin{aligned} & P(A)=2(B) \Rightarrow P(B)=\frac{1}{3} \quad P(A)=\frac{2}{3} \ & 	ext { Required Probability }=\frac{\frac{1}{3} \cdot \frac{4}{7}}{\frac{2}{3} \cdot \frac{3}{5}+\frac{1}{3} \cdot \frac{4}{7}}=\frac{10}{31} .\end{aligned}$