Question

Say the fraction of students at college 1 who took statistics is given by 1/5. Say the fraction of students at college 2 who took statistics is given by 1/2. You survey 10 people from each college (so 20 people in total).

(a) What is the probability that more than half of the surveyed students took statistics from college 1?

(b) What is the probability that more than half of the surveyed students took statistics from college 2?

(c) Assuming that the colleges are independent, what is the probability that more than half of the surveyed students took statistics from college 1 and more than half of the surveyed students took statistics from college 2?

(d) Assuming that the colleges are independent, what is the probability that more than half of the surveyed students took statistics from college 1 or more than half of the surveyed students took statistics from college 2?

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Now say you redo your survey of college 1, but you have not decided how many students to ask, so you just keep asking students indefinitely.

(a) What is the probability that none of the first 3 people have taken statistics?

(b) What is the probability that the first person you find who takes statistics is the 5th person you ask?

(c) What is the probability that the first person you find who takes statistics is the 5th person you ask, given that none of the first 3 people have taken statistics?

Answer 1