In Texas, 30% of released prisoners return to prison within three years of their release. Suppose a prison in Texas released 15 prisoners. Assume that whether one prisoner returns to prison is independent of whether any of the others returns.

(a) Find the probability that exactly 8 out of 15 will end up back in prison within 3 years.

(b) Find the probability that between 7 and 11 will end up back in prison within 3 years.