Door prize. You are among 100 people attending a charity fundraiser at which a large-screen TV will be given away as a door prize. To determine who wins, 99 white balls and 1 red ball have been placed in a box and thoroughly mixed. The guests will line up and, one at a time, pick a ball from the box. Whoever gets the red ball wins the TV, but if the ball is white, it is returned to the box. If none of the 100 guests gets the red ball, the TV will be auctioned off for additional benefit of the charity.
a. What's the probability that the first person in line wins the TV?
b. You are the third person in line. What's the probability that you win the TV?
c. What's the probability that the charity gets to sell the TV because no one wins?
d. Suppose you get to pick your spot in line. Where would you want to be in order to maximize your chances of winning?
e. After hearing some protest about the plan, the organizers decide to award the prize by not returning the white balls to the box, thus ensuring that 1 of the 100 people will draw the red ball and win the TV. Now what position in line would you choose in order to maximize your chances?