Columbia University Probability in Yale University Affiliates Event Problems

Question Description

Suppose that 70% of the people coming out of a particular exit of 19th Street Station are Yale University affiliates. You wait at the exit and ask 10 people whether they are Yale affiliates or not.

(a∗) What is the probability that the third, the fifth and the tenth person are Yale affiliates?
(b∗) What is the probability that the third, the fifth and the tenth person are Yale affiliates and all others are not?
(c∗) What is the probability that you find exactly three Yale affiliates?
(d∗) What is the expected number of Yale affiliates in your sample? What is the variance of this number?
(e∗) Suppose you keep asking people until you find 10 that are not Yale affiliates, and then you go home. How many people do you have to ask on average until you can go home?

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