A bag contains 3 white and 2 black balls, another bag contains some white and 4 black balls. One bag is chosen at random. From the selected bag, one ball is drawn. If the probability of getting a black ball from the selected bag is 8/15, then the number of white balls in the second bag is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2
Let the second bag have w white balls. By the total probability theorem:
\( \displaystyle P(\text{black})=\frac{1}{2}\cdot\frac{2}{5}+\frac{1}{2}\cdot\frac{4}{w+4}=\frac{8}{15} \)
\( \displaystyle \frac{2}{w+4}=\frac{8}{15}-\frac{1}{5} \)
\( \displaystyle =\frac{5}{15}=\frac{1}{3} \)
\( \displaystyle w+4=6 \)
\( \displaystyle w=2 \)