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 executed3.
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