Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with t

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Solution

Q.
Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is $\frac{p}{q}$ , gcd (p,q) = 1, then $p + q$ is equal to [2026]

1 23

2 24

3 21

4 22

Ans.
(1)

[IMAGE 193]

$∴$ $P (Drawn ball is white) = \frac{3}{5} \times \frac{10}{18} + \frac{2}{5} \times \frac{9}{18}$

$= \frac{48}{90} = \frac{8}{15} = \frac{p}{q}$

$∴$ $p + q = 23$

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