Prince Charming has to go around town asking if the glass slipper fits until he finds a woman whose foot fits properly in the slipper so that he will know who to marry. (We do not endorse this technique for finding a wife.) The probability of a glass slipper fitting a randomly selected woman is 0.12, and the probabilities are independent for the various women. Let X be the number of women he has to visit until he finds a woman who fits the slipper. Assume that there are an unlimited supply of eligible women in the town.
a. Given that he has already checked with 4 women without success, what is the probability he will still need to check with at least 5 more? (He's getting impatient.)
b. Given that he has already checked with 4 women without success, what is the probability he will succeed with the very next woman?
c. What is the probability he will succeed on his first try?
d. What is the expected number of women he will have to try?
e. If he takes an entourage with him everywhere he goes, and he has to pay the entourage $100 for the day plus $10 for every visit he makes, how much does he expect to pay if he does all his visits on one day?