Question

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. (Round your answers to three decimal places.)

Answer 1

P(x = 0) = 0.004

P(x = 0) = 0.047

P(x = 0) = 0.211

P(x = 0) = 0.422

P(x = 0) = 0.316

Explanation:

We are given the following information:

We treat a person who does not become a repeat offender as a success.

P(Success) = P(person who does not become a repeat offender) = 0.75

Then the number of people follows a binomial distribution, where

`P(X=x) = \binom{n}{x}.p^x.(1-p)^(n-x)`

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 4

We have to evaluate:

`P(x = 0)\\= \binom{4}{0}(0.75)^0(1-0.75)^4 = 0.004`

`P(x = 1)\\= \binom{4}{1}(0.75)^1(1-0.75)^3 = 0.047`

`P(x = 2)\\= \binom{4}{2}(0.75)^2(1-0.75)^2 = 0.211`

`P(x = 3)\\= \binom{4}{3}(0.75)^3(1-0.75)^1 = 0.422`

`P(x = 4)\\= \binom{4}{4}(0.75)^4(1-0.75)^0 = 0.316`