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4. A genetic study conducted in 2003 indicated that up to 25% of men in one...

4. A genetic study conducted in 2003 indicated that up to 25% of men in one small province of Iran are direct descendants of one individual (historians and vampologists have speculated that it is most likely Nandor the Relentless). Suppose that we select 15 men at random from this province of Iran and observe whether or not this specific Y chromosome sequence occurs in their DNA. We consider a”success” to be an instance in which the individual is a direct descendant of Nandor the Relentless.

(a) What is the probability that there were more than two direct descendants but no more than 6 in this sample?

(b) What is the probability that there were more than 5 direct descendants in our sample?

(c) If we selected 15 men at random from Iran on average how many of them would be direct descendants of Nandor the Relentless (round to two decimal places in your answer).

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