Suppose that 70% of the people coming out of a particular exit of 1000th Street Station are University affiliates. You wait at the exit and ask 10 people whether they are affiliates or not. What is the probability that the third, the fifth and the tenth person are  affiliates? What is the probability that the third, the fifth and the tenth person are  affiliates and all others are not? Suppose you keep asking people until you find 10 that are not  affiliates, and then you go home. How many people do you have to ask on average until you can go home? - You can assume that the status (affiliate or not) of the people coming from the subway are independent. - For the last part: the ten non-affiliates do NOT have to come out consecutively. For example, if you find 9 non-affiliates, then 1 affiliate and then 1 more non-affiliate, that's enough: you can go home.

Suppose that 70% of the people coming out of a particular exit of 1000th Street Station are University affiliates. You wait at the exit and ask 10 people whether they are affiliates or not.

1. What is the probability that the third, the fifth and the tenth person are  affiliates?

2. What is the probability that the third, the fifth and the tenth person are  affiliates and all others are not?

3. Suppose you keep asking people until you find 10 that are not  affiliates, and then you go home. How many people do you have to ask on average until you can go home?

- You can assume that the status (affiliate or not) of the people coming from the subway are independent.

- For the last part: the ten non-affiliates do NOT have to come out consecutively. For example, if you find 9 non-affiliates, then 1 affiliate and then 1 more non-affiliate, that's enough: you can go home.