SOLUTION: USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a perso

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Question 375850: USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a person does not become a repeat offender. Alice has been given a group of four parolees.
(a) Find the probability P(r) of r successes ranging from 0 to 4.
P(0) =
P(1) =
P(2) =
P(3) =
P(4) =
What is the expected number of parolees in Alice's group who will not be repeat offenders? What is the standard deviation?
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi
Note: The probability of x successes in n trials is:
P = nCx* where p and q are the probabilities of success and failure respectively.
In this case p = .75 & q = .25
nCx =
P(0) = .25^4 = .0039
P(1) = 4(.75)(.25)^3 = .0469 4C1 = 4
P(2) = 6(.75)^2(.25)^2 = .2109 4C2 = 6
P(3) = 4(.75)^3(.25)1 = .4219 4C3 = 4
P(4) = (.75)^4 = .3164
.75*4 = 3 will not be repeat offenders