In: Statistics and Probability
4) A pediatrician wishes to recruit 4 couples, each of whom is expecting their first child, to participate in a new natural childbirth regimen. Let p = 0.2 represent the probability that a randomly selected couple agrees to participate.
a) What is the probability that 15 couples refuse to participate before 4 are found who agree to participate?
b) What is the probability that 12 couples refuse to participate before 4 are found who agree to participate?
c) What is the expected value of the total number of couples that must be asked to have 4 participating couples?
d) What is the variance of the total number of couples that must be asked to have 4 participating couples.