In a region there is a 0.9 probability chance that a randomly selected person of

Question

In a region there is a 0.9 probability chance that a randomly selected person of the population has brown eyes. Assume 10 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 10 selected people have brown eyes is 349. (Round to three decimal places as needed.) b Find tie probability tot exactly 9 of the selected people have brown eyes. The probability that exactly 9 of the selected people have brown eyes is. (Round to three decimal places as needed.) c. Find to probability that to number of selected people that have brown eyes is 8 or more. The probability tot to number of selected people that have brown eyes is 8 or more is. (Round to three decimal places as needed.) d. If 10 people are randomly selected is 8 an unusually high number for those with brown eyes? Yes, because to probability tot 8 or more of to selected people have brown eyes is less than 0.05. Yes, because to probability tot 8 or more of the selected people have brown eyes is greater than 0.05. No, because to probability that 8 or more of these selected people have brown eyes is greater than 0.05. No, because to probability that 8 or more of to selected people have brown eyes is less than 0.05.

Explanation / Answer

Let X denote the RV for number of persons with brown eyes

Here p = 0.9

(a)

P(X=10) = 10C10*p10*(1-p)10-10 = 1*0.910*(1-0.9)10-10 = 0.349

(b)

P(X=9) = 10C9*p9*(1-p)10-9 = 10*0.99*(1-0.9)10-9 = 0.387

(c)

P(X >= 8) = P(X=8) + P(X=9) + P(X=10)

P(X=8) = 10C8*p8*(1-p)10-8 = 45*0.98*(1-0.9)10-8 = 0.193

So,

P(X >= 8) = 0.193 + 0.387 + 0.349 = 0.929

(d)

NO, because the probability that 8 or more of the selected people have brown eyes is greater than 0.05

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