Question

One bag contains $5$ white and $4$ black balls. Another bag contains $7$white and $9$ black balls. A ball is transferred from the first bag to the second and then a ball is drawn from second. The probability that the ball is white is

• A. $\frac{8}{17}$
• B. $\frac{40}{153}$
• C. $\frac{5}{9}$
• D. $\frac{4}{9}$

Answer 1

The correct option is D

$\frac{4}{9}$

Explanation for the correct option:

Finding the probability that the ball is white is:

Given: One bag contains $5$ white and $4$ black balls. Another bag contains $7$white and $9$ black balls.

Therefore total number of balls in bag one is $9$ and bag two is $16$

The probability of selecting white ball from first bag$=\frac{5}{9}$

The probability of selecting black ball from first bag$=\frac{4}{9}$

If a white ball is transferred from first bag to second bag, then the probability of selecting white ball from second $=\left(\frac{8}{17}\right)$

If a black ball is transferred from first bag to second, then the probability of selecting white ball from second is $=\left(\frac{7}{17}\right)$

Now probability of drawing white ball from second bag

$=\frac{5}{9}\times \frac{8}{17}+\frac{4}{9}\times \frac{7}{17}$

$=\left(\frac{40}{153}\right)+\left(\frac{28}{153}\right)=\frac{4}{9}$

Hence the correct answer is option (D).