Question

A bag $A$ contains $3$ white and $2$ black balls and another bag $B$ contains $2$ white and $4$ black balls. $A$ bag and a ball out of it are picked at random. What is the probability that the ball is white?

• A. $\frac{14}{15}$
• B. $\frac{8}{15}$
• C. $\frac{1}{15}$
• D. $\frac{7}{15}$

Answer 1

Answer: (D)

$\frac{7}{15}$

Bag $A$ has $3W,2B$.
Bag $B$ has $2W,4B$.
Probability of selecting a bag is $\frac{1}{2}$.
$\text{Required probability}=\text{Probability of selecting white ball from bag A}$ or $\text{Probability of selecting white ball from bag AB}$
$=\frac{1}{2}.\frac{3}{5}+\frac{1}{2}.\frac{2}{6}$
$=\frac{7}{15}$