Scoring a hole-in-one is the greatest shot a golfer can make. Once 5 professiona

Question

Scoring a hole-in-one is the greatest shot a golfer can make. Once 5 professional golfers each made holes-in-one on the 7^th hole at the same golf course at the same tournament it has been found that the estimated probability of making a hole-in-one is for make professionals. Suppose that a sample of 5 professional male golfers is randomly selected. (a) What is the probability that all of these golfers make a hole-in-one on the 12^th hole at the same tournament? (b) What is the probability that none of these golfers make a hole-n-one on the 12^th hole at the same tournament?

Explanation / Answer

the probability of scoring a hole in one is 1/2792 for male professionals.

now 5 male professionals are chosen in random.

hence their scoring ability is independent of each other.

a) so the probability that all of them scored a hole in one is

P[1st professional scored a hole in one]*P[2nd professional scored a hole in one]*....*P[5th professional scored a hole in one]=(1/2792)5   [answer]

b) probability that none of them scored a hole in one is

P[first professional did not score a hole in one]*P[second professional did not score a hole in one]*...*P[5th professional did not score a hole in one]=(1-1/2792)5=(2791/2792)5  [answer]

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