Fred is a left-handed person who walks into a large lecture room for a 4-hour exam. He's a little absent-minded at the moment because he's worried about the exam. He needs to find a left-handed desk to sit in for the exam or else his back will get cramped up before the exam is over, but he won't know if the desk is left-handed until he actually sits in one, because the desk part folds underneath the chair. Ten percent of the desks in the exam room are for left-handed people, and the choice of left-or-right handedness is independent from desk to desk, throughout the room. Assume Fred is the first student to walk in the door.
a. What is the probability that Fred finds his first left-handed desk on his 5th try?
b. If Fred keeps sampling desks to find the left-handed desk which "feels lucky," what is the probability he finds his 3rd left-handed desk on his 8th try?
c. What is the average number of desks Fred has to try until finding his 2nd left-handed desk?
d. If the first 9 desks tested are not left-handed, what is the probability that he has to keep looking for more than 12 desks total to find his first left-handed desk?