Homework 5-KIM D\'ADDONA 17. In a region, there is a 0.9 probability chance that
ID: 3306890 • Letter: H
Question
Homework 5-KIM D'ADDONA 17. In a region, there is a 0.9 probability chance that a randomly selected person of the population has brown eyes. Assume Page 9 of 15 2 people are randomly selected. Complete parts (a) through (d) below a. Find the probability that all of the selected people have brown eyes The probability that all of the 12 selected people have brown eyes is (Round to three decimal places as needed.) b. Find the probability that exactly 11 of the selected people have brown eyes The probability that exactly 11 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 10 or more The probability that the number of selected people that have brown eyes is 10 or more is (Round to three decimal places as needed) d. If 12 people are randomly selected, is 10 an unusually high number for those with brown eyes? 0 A. B. ° C. No, because the probability that 10 or more of the selected people have brown eyes is greater than 0.05 Yes, because the probability that 10 or more of the selected people have brown eyes is greater than 0.05 Yes, because the probability that 10 or more of the selected people have brown eyes is less than 0.05 No, because the probability that 10 or more of the selected people have brown eyes is less than 0.05 D.Explanation / Answer
a. The probability that all people selected have brown eyes = 0.912 = 0.282
b. The one person who does not have brown eyes can come in 12 different ways
Probability that exactly 11 have brown eyes = 12 * 0.911 * 0.1 = 0.377
c. If two people do not have brown eyes they can be selected in 12C2 = 66 ways
Probability that exactly 10 have brown eyes = 66 * 0.910 * 0.12 = 0.230
=> Probability that atleast 10 have brown eyes = 0.282 + 0.377 + 0.230 = 0.889
d. The answer is A. No. Because the probability that 10 or more people have brown eyes is more than 0.05
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