Question

A bag contains 2 white balls and 4 black balls. Another bag contains 3 white and 2 black balls. A bag and a ball are picked randomly. The probability that the ball will be white is:

• A. 8/15
• B. 7/15
• C. 3/10
• D. 1/6
• E. none

Answer 1

The correct option is B

7/15

The probability of selecting one bag = $\frac{1}{2}$
Now, probability of getting a white ball from bag A: $\frac{1}{2}$$\times$$\frac{3}{5}$ = $\frac{3}{10}$
and probability of getting a white ball from bag B: $\frac{1}{2}$$\times$$\frac{2}{6}$ = $\frac{1}{6}$
Hence, Probability that white ball is drawn either first or second bag: $\frac{3}{10}$+$\frac{1}{6}$ =$\frac{7}{15}$