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. Find the probability P(r) of r successes ranging from 0 to 4. (Round your answers to three decimal places.)

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 1

P(0) = 4C0 * 0.75⁰ * 0.25⁴ = 0.00390625 . = 0.004

P(1) = 4C1 * 0.75¹ * 0.25³ = 0.046875 . . . = 0.047

P(2) = 4C2 * 0.75² * 0.25² = 0.2109375 . . = 0.211

P(3) = 4C3 * 0.75³ * 0.25¹ = 0.421875 . . . = 0.422

P(4) = 4C4 * 0.75⁴ * 0.25⁰ = 0.31640625 . = 0.316

Check:

P(0) + P(1) + P(2) + P(3) + P(4) = 1 . . . ok

Explanation: