Question

A bag contains black and yellow marbles. Two marbles are drawn without replacement. The probability of selecting a black marble and then a yellow marble is 0.28. The probability of selecting a black marble on the first draw is 0.5. What is the probability of selecting a yellow marble on the second draw, given that the first marble drawn was black?

A) 0.28
B) 0.56
C) 0.64
D) 0.78

Answer 1

To find the probability of selecting a yellow marble on the second draw, given that the first marble drawn was black, we can use conditional probability. The probability of selecting a yellow marble on the second draw, given that the first marble drawn was black, is 0.56.

Step-by-step explanation:

To find the probability of selecting a yellow marble on the second draw, given that the first marble drawn was black, we can use conditional probability. Conditional probability is calculated by dividing the probability of the intersection of the two events (selecting a black marble and then a yellow marble) by the probability of the first event (selecting a black marble).

Let's denote the event of selecting a black marble as A and the event of selecting a yellow marble on the second draw as B. So we want to find P(B|A), which represents the probability of B given A.

From the given information, we know that P(A) = 0.5 and P(A∩B) = 0.28. To calculate P(B|A), we can use the formula P(B|A) = P(A∩B) / P(A).

Substituting the given values, we get P(B|A) = 0.28 / 0.5 = 0.56.