The Augusta National Golf Course in Augusta, Georgia hosts the Masters Tournament each April. The course consists of four par 3s, ten par 4s, and four par 5s. The par 4s and par 5s are long enough so that no golfer has a realistic chance of getting a hole in one, but the par 3s are each short enough so that the possibility of a hole in one does exist. Over the 75-year history of the tournament, golfers have teed off on par 3s approximately 70,000 times, and a total of 73 holes in one have been recorded. For a given golfer, suppose the probability of getting a hole in one on each of the par 3s at Augusta are as follows:
Hole Number P(hole in one)
a. For a randomly selected golfer, find the probability of no holes in one during a round of golf. Assume independence from one hole to the next.
b. For a randomly selected golfer, find the probability of no holes in one during the next 20 rounds of golf. Assume independence from one round to the next.
c. Use your answer in part b to find the probability of making at least one hole in one during the next 20 rounds of golf.