Urn A has 3 white and 8 red balls. Urn B has 10 white and 14 red balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected. Suppose that a white ball is selected. What is the probability that the coin landed heads?

The probability that the coin landed heads given that a white ball is selected is 0.3957.

Step-by-step explanation:

Let W = a white ball is selected.

Balls in Urn A = 3 white and 8 red = 11 balls.

Balls in Urn B = 10 white and 14 red = 24 balls.

A coin is tossed to select an urn.

If the coin turns up Heads urn A is selected and if it turns up Tails urn B is selected.

P (A) = P(B) = 0.50

Compute the probability that a white ball is selected as follows:

P (W) = P (W ∩ A) + P(W ∩ B)

        = P (White from A)×P (A) + P (White from B)×P (B)

The probability of selecting a white ball is P (W) = 0.3447.

If the coin lands Heads it implies that urn A was selected.

Then compute the probability that urn A is selected given that a white ball was selected as follows:

Thus, the probability that the coin landed heads given that a white ball is selected is 0.3957.