In: Statistics and Probability
Say the fraction of students at college 1 who took statistics is given by 1/4. Say the fraction of students at college 2 who took statistics is given by 3/5. You survey 10 people from each college (so 20 people in total).
(a) What is the probability that more than half of the students surveyed from college 1 took statistics?
(b) What is the probability that more than half of the students surveyed from college 2 took statistics?
(c) Assuming that the colleges are independent, what is the probability that more than half of the students surveyed from college 1 took statistics and more than half of the students surveyed from college 2 took statistics?
(d) Assuming that the colleges are independent, what is the probability that more than half of the students surveyed from college 1 took statistics, or more than half of the students surveyed from college 2 took statistics?