Please only solve part a.

Please write step by step solution with the correct calculation. Please make sure that you understand the question completely. You do not need to type. You can just scan the solution. Thank you.

A bus driver randomly selects a coin from the following choices: . Coin A: a fair coin with P(Head) = 1/2 . Coin B: a biased coin with P(Head) = 1/3 . Coin C: a biased coin with P(Head) = 1/4 (a) What is the probability that she needed at least 5 coin flips to get the first Head? Assume that all flips are done with the same coin and that the flips are all independent of each other. (b) Given that she needed less than 3 coin flips to see the first Head, what is the probability she selected Coin A? What about Coin B? Coin C? Assume that all coin flips are independent of each other