Chapter 5, Problem 86CP

Death penalty and false positives For the decision about whether to convict someone charged with murder and give the death penalty, consider the variables reality (defendant innocent, defendant guilty) and decision (convict, acquit).

1. a. Explain what the two types of errors are in this context.
2. b. Jurors are asked to convict a defendant if they feel the defendant is guilty beyond a reasonable doubt. Suppose this means that given the defendant is executed, the probability that he or she truly was guilty is 0.99. For the 1234 people put to death from the time the death penalty was reinstated in 1977 until December 2010, find the probability that (i) they were all truly guilty, and (ii) at least one of them was actually innocent.
3. c. How do the answers in part b change if the probability of true guilt is actually 0.95?