Suppose the new debate format for Rodham and Drumpf is as follows: On the candidate's turn, the candidate must pick either challenge A or B. In challenge A, the candidate is forced to answer a question which he/she has a 1/2 probability of answering correctly. If answered correctly, the candidate will be rewarded the presidency. If answered incorrectly, the candidate will be forced to eat spoiled cheese. In challenge B, the candidate will be forced to complete a physical task which he/she has 1/3 chance of completing. If the candidate succeeds, he/she will rewarded a Justin Bieber CD. If the candidate does not suc-ceed, he/she will be forced to eat spoiled cheese.

(a) Rodham decides to flip a biased coin with probability 2/3 of getting heads to decide which challenge to take: heads means she takes A, tails means she takes B. Given that she is forced to cat spoiled cheese after her turn, what is the probability that she selected challenge A?

(b) Suppose Drumpf is equally likely to pick challenge A or challenge B on his turn. What is the probability that he does not win the presidency on his turn?

(c) Suppose candidate Rodham goes first, and suppose the candidates take turns playing this game until one of the candidates is rewarded the presidency (at which time the debate stops). What is the probability that Rodham wins the presidency on her kth turn?