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In: Statistics and Probability

4) A pediatrician wishes to recruit 4 couples, each of whom is expecting their first child,...

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.

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