Coins and dice. Consider the following game: The player flips a fair coin. If it shows a head, he gets to roll a 4-sided die. If it shows a tail, he gets to roll a 6-sided die. In either case, let A denote the event that he gets 1 on the die roll. Let H denote the event that his coin flip shows a head, i.e., that he uses the 4-sided die. Let T denote the event that his coin flip shows a tail, i.e., that he uses the 6-sided die.

a. Find P(H | A).

b. Find P(T | A).

Hint: To verify your answers, note P(H | A) + P(T | A) = 1.