This is stats 131 from UCSC. Thanks for your help :)

3. [30 points] (logic and Bayes's Theorem) Here's a small ctitious drama with ve actors: three people A, B and C on death row; the governor, who has chosen one of them at random to be pardoned; and a warden in the prison, who knows the identity of the person the governor picked but isn't allowed to tell A, B or 0 who the lucky person will be. Person A now speaks to the warden, as follows. Please tell me the name of one of the other prisoners who's not going to be pardoned no harm done, since you won't be identifying the lucky person. Let's agree on these rules: if B will be pardoned, you say 0; if C will get the pardon, you say B; and if I'm the lucky person, you toss a 50/50 coin to decide whether to say B or C. '3 The warden thinks it over and says \"B won't get the pardon. This is good news to A, because he secretly didn't believe that the warden's statement contains no information relevant to him: he thinks that, given what the warden said, his chance for the pardon has gone up from g to :7. Use Bayes's Theorem to show that A's reasoning is incorrect, thereby working out whether there was information in what the warden said that's relevant to A's probability of being pardoned. [25 points]