Suppose we take an additional 7 trials, and achieve 2 successes.

(a) Let the posterior after the 8 trials and 3 successes in the previous problem be the prior and use BinoDP.mac or the equivalent R function to find the new posterior distribution for π.

(b) In total, we have taken 15 trials and achieved 5 successes. Go back to the original prior and use BinoDP.mac or the equivalent R function to find the posterior after the 15 trials and 5 successes.

(c) What does this show?