Three prisoners, named Al, Bob and Chuck, are informed by their jailer that one of them has been

Three prisoners, named Al, Bob and Chuck, are informed by their jailer that one of them has been chosen at random to be executed, and the other two are to be freed. Al asks the jailer to tell him privately which of his fellow prisoners will be set free, claiming that there would be no harm in divulging this information, since he already knows that at least one will go free.

a) Assume that if both Bob and Chuck will be set free, then the jailer flips a fair coin to decide which name to tell Al. Suppose the jailer tells Al that Bob will be set free. Whar is the probability that Al will be executed?

b) Assume that if both Bob and Chuck will be set free, then the jailer (a firm believer in proper aplhabetical ordering) will pick Bob's name to tell Al. Suppose the jailer tells Al that Bob will be set free. What is the probability that Al will be executed?

c) Assume that if both Bob and Chuck will be set free, then the jailer (happy owner of a biased - Euro? - coin, picks Bob's name with probability q and Chuck's name with probability 1-q. Suppose the jailer tells Al that Bob will be set free. What is the probability that Al will be executed

3. Fischer and Spassky play a chess match in which the first player to win a game wins the match. After 10 successive draws, the match is declared drawn. Each game is won by Fischer with probability 0.4, is won by Spassky with probability 0.3, and is a draw with probability 0.3, independently of previous games.

a) What is the probability that Fischer wins the match?

b) What is the PMF of the duration of the match?

4. Consider a traingle and a point chosen within the traingle according to the uniform probability law. Let X be the distance from the point to the base of the traingle. Given the height of the traingle, find the CDF and the PDF of X