Below is the complete problem. I already have answers for parts a, b, and d. I can't figure out the answers to part c -- there are actually 2 questions in part c.

(a)Given that Bob observed k Heads out of the 3 tosses (where k = 0, 1, 2, 3), what is the conditional probability that he received the first coin?

(b)We define an error to have occurred if Bob decides that he received one coin from Alice, but he actually received the other coin. He decides that he received the first coin when the number of Heads, k, that he observes on the 3 tosses satisfies a certain condition. Find the condition that will minimize the probability of error.

(c)For this part, assume that p = 2/3. What is the probability that Bob will guess the coin correctly using the decision rule from part (b)?

Suppose instead that Bob tries to guess which coin he received without tossing it. He still guesses the coin in order to minimize the probability of error. What is the probability that Bob will guess the coin correctly under this scenario?

(d)Suppose that Bob uses the decision rule in part (b) to guess the coin. Find the values of p for which Bob will never decide that he received the first coin, regardless of the outcome of the 3 tosses.