Question

A​ state's recidivism rate is 17​%. This means about 17​% 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 nothing​%. ​(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.

Answer 1

Answer:

a) 2.9%

b) Option B is correct.

The prisoners must be independent with regard to recidivism.

Step-by-step explanation:

Probability that one prisoner goes back to prison = 17% = 0.17

a) The probability that two prisoners released both go back to prison = 0.17 × 0.17 = 0.0289 = 2.89% = 2.9% to 1 d.p

b) The only assumption taken during the calculation is that probability of one of the prisoners going back to prison has no effect whatsoever in the probability that another prisoner goes back to prison. That is the probability that theses two events occur are totally independent of each other.

If they weren't, we wouldn't be able to use 0.17 as the probability that the other prisoner goes back to prison too.