Peter and Maryam take turns throwing one dart at the dartboard. Peter hits the bullseye with probability 1/5 and Maryam hits the bullseye with probability 1/3. Each throw is independent of the last. Whoever hits the bullseye first wins. Suppose Peter throws the first dart.
What is the probability that Maryam wins on her first throw? (Hint: This means that Peter's first throw misses and Maryam's first throw hits.)Prob =
What is the probability that Maryam wins on her kth throw? (Your answer will be in terms of k.)Prob =
What is the probability Maryam wins?Prob =