14. A game at a fund-raiser: There are 20 rubber
ducks floating in a pool. One of the ducks has a
mark on the bottom, indicating that the contestant
wins a prize. Each contestant pays 25 cents to play.
A contestant randomly picks 2 of the ducks. If the
contestant picks the duck with the mark on the
bottom, the contestant wins a prize that costs $1.
a. What is the probability that a contestant will
win a prize? Explain.
b. If 200 people play the game, about how many
people would you expect to win? Why?
c. Based on your answer to part (b), how much
money should the duck game be expected to
earn for the fund-raiser (net) if 200 people play
it? Explain.