In a region, there is a 0.95 probability chance that a randomly selected person

Question

In a region, there is a 0.95 probability chance that a randomly selected person of the population has brown eyes. Assume 13 people are randomly selected. Complete parts (a) through (c) below. a. Find the probability that all of the selected people have brown eyes The probability that all of the 13 selected people have brown eyes is The probability that ll of the 13 selected people have brown eyes is Round to three decimal places as needed.) b. Find the probability that exactly 12 of the selected people have brown eyes The probability that exactly 12 of the selected people have brown eyes is (Round to three decimal places as needed.) c. Find the probability that the number of selected people that have brown eyes is 11 or more. The probability that the number of selected people that have brown eyes is 11 or more is Round to three decimal places as needed.)

Explanation / Answer

This will be a binomial distribution with parameters:

n = 13, p = 0.95

Hence,

a) P(All 13) = (0.95)13 = 0.513

b) P(Exactly 12) = 13C12 * 0.05 * (0.95)12 = 0.351

c) P(11 or more) = P(11) + P(12) + P(13) = 13C11 * 0.052 * (0.95)11 + 13C12 * 0.05 * (0.95)12 + (0.95)13 = 0.975

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