Question

A jar contains black and white marbles. Two marbles are chosen without replacement. The probability of selecting a black marble and then a white marble is 0.39, and the probability of selecting a black marble on the first draw is 0.52. What is the probability of selecting a white marble on the second draw, given that the first marble drawn was black?75%65%25%100%

Answer 1

It is given that the probability of selecting a black marble and then a white marble is 0.39 and that the probability of selecting a black marble on the first draw is 0.52.

It is required to find the probability of selecting a white marble on the second draw, given that the first marble drawn was black.

Let the event "drawing a black marble" be A and let the event "drawing a white marble" be B.

Since it is given that the probability of selecting a black marble and then a white marble is 0.39, it follows that:

$P(A\text{ and }B)=0.39$

Since the probability of selecting a black marble on the first draw is 0.52, it follows that:

$P(A)=0.52$

Recall the Conditional Probability Formula for the probability of B occurring given A has occurred:

$P(B|A)=\frac{P(A\text{ and }B)}{P(A)}$

Substitute P(A and B)=0.39 and P(A)=0.52 into the formula:

$\Rightarrow P(B|A)=\frac{0.39}{0.52}=0.75=75\%$

The answer is 75%.