Thirteen cards are dealt from a deck of 52 cards.
(a) What is the probability that the ace of spades is one of the 13 cards?
(b) Suppose that one of the 13 cards is chosen at random and found not to be the ace of spades. What is the probability that none of the 13 cards is the ace of spades?
(c) Suppose that the experiment in part (b) is repeated a total of 10 times (replacing the card looked at each time) and the ace of spades is not seen. What is the probability that the ace of spades actually is one of the 13 cards?
Use Bayes' theorem to calculate the probabilities?