Question

A bag contains 3 black balls and 5 white balls. Paul picks a ball at random from the bag and replaces it back in the bag. He mixes the ball inn the bag and then picks another bag at random from the bag. Find what is the probability that Paul draws the first and second ball matching in color?

a. 17/64
b. 1/8
c. 5/12
d. 3/16

Answer 1

To find the probability that Paul draws the first and second ball matching in color, we need to consider the probabilities of drawing the same color ball twice. The probability of drawing two black balls is 9/64 and the probability of drawing two white balls is 25/64. The total probability is 17/32 or 17/64.

Step-by-step explanation:

To find the probability that Paul draws the first and second ball matching in color, we need to consider the probabilities of drawing the same color ball twice. In this case, there are two possibilities: drawing two black balls or drawing two white balls. Let's calculate the probability for each case:

1. Probability of drawing two black balls:
   The probability of drawing a black ball in the first draw is 3/8 (there are 3 black balls out of 8 total balls). Since the ball is replaced, the probability of drawing another black ball in the second draw is also 3/8. Therefore, the probability of drawing two black balls is (3/8) * (3/8) = 9/64

1. Probability of drawing two white balls:
   The probability of drawing a white ball in the first draw is 5/8 (there are 5 white balls out of 8 total balls). Since the ball is replaced, the probability of drawing another white ball in the second draw is also 5/8. Therefore, the probability of drawing two white balls is (5/8) * (5/8) = 25/64.

Now, we can find the total probability of drawing the first and second ball matching in color by adding the probabilities of the two cases:

Total probability = (Probability of drawing two black balls) + (Probability of drawing two white balls) = 9/64 + 25/64 = 34/64 = 17/32

Therefore, the correct answer is a. 17/64.