Urn A contains six white balls and three black balls. Urn B contains seven white balls and five black balls. A ball is drawn from Urn A and then transferred to Urn B. A ball is then drawn from Urn B. What is the probability that the transferred ball was white given that the second ball drawn was white? (Round your answer to three decimal places.)

determine the probability of selecting 2 red marbles. selecting


a box contain 7 black ,3 red, and 5 purple marbles consider the two- stage experiment of randomly selecting a marble from the box

To calculate the probability that the transferred ball was white given that the second ball drawn was white, we need to use conditional probability.

Step 1: Determine the individual probabilities:
The probability of drawing a white ball from Urn A is 6/9 (6 white balls out of a total of 9 balls).
The probability of drawing a black ball from Urn A is 3/9 (3 black balls out of a total of 9 balls).

Step 2: Calculate the probability of transferring a white ball from Urn A to Urn B:
Since there are 6 white balls in Urn A, when one white ball is transferred to Urn B, Urn A will have 5 white balls left.
Consequently, there are now 10 balls in Urn B, of which 7 are white and 3 are black.
Therefore, the probability of transferring a white ball from Urn A to Urn B is 6/10 (6 white balls out of a total of 10 balls in Urn B).

Step 3: Determine the probability of drawing a white ball from Urn B after the transfer:
The probability of drawing a white ball from Urn B, given that one white ball was transferred from Urn A, is 7/10 (since there are 7 white balls out of a total of 10 balls in Urn B).

Step 4: Calculate the conditional probability:
Conditional probability is given by the formula:
P(A|B) = P(A and B) / P(B)
where P(A|B) is the probability of event A given that event B has occurred, P(A and B) is the probability of both events A and B happening, and P(B) is the probability of event B happening.

In this case, event A is transferring a white ball from Urn A to Urn B, and event B is drawing a white ball from Urn B.

Therefore, the probability that the transferred ball was white given that the second ball drawn was white is:
P(Transferred ball white | Second ball white) = (P(Transferred ball white and Second ball white)) / P(Second ball white)

To determine P(Transferred ball white and Second ball white):
Since the transferred ball being white and the second ball being white are independent events, the probability of both events happening is simply the product of their individual probabilities:
P(Transferred ball white and Second ball white) = (6/10) * (7/10)

To determine P(Second ball white):
This is already given as 7/10.

Plugging these values into the formula, the probability that the transferred ball was white given that the second ball drawn was white is:
P(Transferred ball white | Second ball white) = (6/10 * 7/10) / (7/10) = 6/10 ≈ 0.600.

Therefore, the probability that the transferred ball was white given that the second ball drawn was white is approximately 0.600 or 60.0%.