During the 2nd round of the 1989 U.S. open, 4 golfers made holes in one on the 6

Question

During the 2nd round of the 1989 U.S. open, 4 golfers made holes in one on the 6th hole. According to the experts, the odds against a professional golfer making a hole in one are 3708 to 1; in other words the probability is 1/3709 that a pro golfer will make a hole in one.  155 golfers participated in the 2nd round.
--Determine the probablity that at least 4 out of 155 golfers would get a whole in one on the 6th hole. Discuss your result. --What assumptions were made? Are the assumptions reasonable? Explain. During the 2nd round of the 1989 U.S. open, 4 golfers made holes in one on the 6th hole. According to the experts, the odds against a professional golfer making a hole in one are 3708 to 1; in other words the probability is 1/3709 that a pro golfer will make a hole in one.  155 golfers participated in the 2nd round.
--Determine the probablity that at least 4 out of 155 golfers would get a whole in one on the 6th hole. Discuss your result. --What assumptions were made? Are the assumptions reasonable? Explain.

Explanation / Answer

The probability that 0 golfer makes a whole in one is (3708/3709)^155 = 0.95907 The probability that 1 golfer makes a whole in one is (1/3709)/(3708/3709)^154 * (155 choose 1) = 0.04009 The probability that 2 golfer makes a whole in one is (1/3709)^2/(3707/3709)^153 * (155 choose 2) = 0.00083 The probability that 3 golfer makes a whole in one is (1/3709)^3/(3707/3709)^152 * (155 choose 3) = 0.00001 Then P(B'0 union B'1 union B'2 union B'3) = P(B'0) + P(B'1) + P(B'2) + P(B'3) P(B') = 0.99999 And P(B) = 1 - P(B') = 0.00001 Discuss : Wow, 4 golfers making a hole in one? That's impossible! Assumptions : We assumed that all our events were independant, which is highly reasonable as assumptions because I don't see how one golfer would affect the other. I also assumed that B'0, B'1, etc are mutually exclusive but that's obvious because we can't have 1 golfer making a hole in one as the same time as 2.

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