Q. A bag $X$ contains 2 white and 3 black bails and another bag $Y$ contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then, the probability for the ball chosen be white, is
A) $\frac{2}{15}$
B) $\frac{7}{15}$
C) $\frac{8}{15}$
D) $\frac{14}{15}$
Explanation
(c)
Probability of selecting a white ball from $X$ bag$= \frac{2}{5}$
Probability of selecting a white ball from $Y$ bag
$= \frac{4}{6} = \frac{2}{3}$
Probability of selecting a white ball from $X$ or $Y$ bags
$= \frac{2}{5} + \frac{2}{3} = \frac{16}{15}$
Probability of selecting the white ball from one of the bags
$= \frac{1}{2}.\frac{16}{15} = \frac{8}{15}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.