Question

A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, then the probability that one ball is white and one ball is black is

• A. $\frac{5}{24}$
• B. $\frac{13}{24}$
• C. $\frac{1}{4}$
• D. $\frac{2}{3}$

Answer 1

Answer: (B)

$\frac{13}{24}$

Solution:

$P$(one ball is white and one ball is black)$=P$(black ball from bag 1 and white ball from bag 2 or white ball from bag 1 and black ball from bag 2)

$=\frac{2}{6}\times \frac{3}{8}+\frac{4}{6}\times \frac{5}{8}$

$=\frac{26}{48}=\frac{13}{24}$

Hence, B is the correct option.