Scoring a hole-in-one is the greatest shot a golfer can make. Once 8 professiona

Question

Scoring a hole-in-one is the greatest shot a golfer can make. Once 8 professional golfers each made holes-in-one on the 8th 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 12603for male professionals. Suppose that a sample of 8 professional male golfers is randomly selected. Be sure to give your answers to at least 4 decimal places.

what is the probability that at least one of these golfers makes a hole-in-one on the 15th hole at the same tournament?

What is the probability that none of these golfers make a hole-in-one on the 15th hole at the same tournament?

Explanation / Answer

As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)

here p = 1/2603

P(none of the golfers makes a hole in one) = (1-p)^15
= (2602/2603)^8 = 0.9969

Hence required probability, P(at least one) = 1 - 0.9969 = 0.0031

P(none) = 0.9969
P(at least one) = 0.0031

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