Answer:
The probability that the coin landed heads is 65.3%.
Explanation:
Given : Urn A has 5 white and 17 red balls. Urn B has 9 white and 12 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.
To find : What is the probability that the coin landed heads ?
Solution :
Let the event A be the ball taken from Urn A (5 white and 17 red balls)
Let B=A'- the ball taken from urn B(9 white and 12 red balls)
Let W be event that a white ball is selected.
An urn is chosen based on a toss of a fair coin.
P(A) = coin landed on heads =

P(B) = coin landed on tails =

and

Using Bayes formula,








Therefore, the probability that the coin landed heads is 65.3%.