Question

A bag contains 4 white and 5 black balls. Another bag contains 9 white and 7 black balls. A ball is transferred from the first bag to the second, and then a ball is drawn at random from the second bag. Find the probability that the ball drawn is white.

a. 4/15​
b. 7/20​
c. 9/20​
d. 3/8​

Answer 1

The probability of drawing a white ball from the second bag after transferring a ball from the first is calculated using the law of total probability. Considering both scenarios of transferring a white or black ball and then drawing from the second bag, the total probability is found to be 7/20.

Step-by-step explanation:

The question deals with the probability of drawing a white ball from the second bag after transferring one ball from the first bag to the second bag. We need to calculate the total probability by considering the two scenarios where the transferred ball is white or black. Here's the step-by-step process:

1. Calculate the probability of transferring a white ball: There are 4 white balls and 5 black balls in the first bag, so the probability is 4 out of 9 (4/9).
2. After transferring a white ball, the second bag will have 10 white and 7 black balls, so the probability of then drawing a white ball is 10 out of 17 (10/17).
3. Calculate the probability of transferring a black ball, which is 5 out of 9 (5/9).
4. After transferring a black ball, the second bag will have 9 white and 8 black balls, so the probability of then drawing a white ball is 9 out of 17 (9/17).
5. Use the law of total probability to combine these two scenarios: (4/9) * (10/17) + (5/9) * (9/17), which simplifies to 7/20.

Therefore, the probability that the ball drawn from the second bag is white is 7/20, which makes option b the correct answer.