Question

The dorm in which you live houses 2% of the total student population. You know 40% of the students living in your dorm, but you know only 5% of the rest of the population. A lot of students (including yourself) go to a party, and you are seated at a table with 3 other people. The number of people is very large, so you can assume that the events of knowing different people at the party are independent.

a. For i = 0; 1; 2; 3, what is the probability of you sitting with i people that you know?

b. Given that i students (where i = 0; 1; 2 or 3) from your dorm are sitting at your table, what is the probability that you know all the people at your table?

c. The host tells you that you are seated at a table with 3 other people you know. What is the probability that all these three students at your table are from your dorm?

Answer 1