A state\'s recidivism rate is 27%. This means about 27% of released prisoners en

Question

A state's recidivism rate is 27%. This means about 27% of released prisoners end up back in prison (within three years). Suppose two randomly selected prisoners who have been released are studied. Complete parts (a) through (c) below.

a. What is the probability that both of them go back to prison? What assumptions must you make to calculate this?

The probability that both of them go back to prison is__%. (Round to one decimal place as needed.)

What assumptions must you make to calculate this?

A. The prisoners cannot be independent with regard to recidivism.

B. The prisoners must be independent with regard to recidivism.

C. The two prisoners cannot be selected at the same time.

D. No assumptions are necessary.

b. What is the probability that neither of them goes back to prison?

The probability that neither of them goes back to prison is __%. (Round to one decimal place as needed.)

c. What is the probability that at least one goes back to prison?

The probability that at least one goes back to prison is __%. (Round to one decimal place as needed.)

Explanation / Answer

Here p = 0.27

a)
Here the assumption is "The prisoners must be independent with regard to recidivism."

Hence, the probability that both of them go back to prison is 0.27*0.27 = 0.0729 i.e. 7.29%

b)
Probability that neither of them goes back to prison = (1-0.27)*(1-0.27) = 0.5329 i.e. 53.29%

c)
at least one goes back to prison = 1 - P(neither of them goes back to prison)
= 1 - 0.5329 = 0.4671 i.e. 46.71%

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