A coin collector who is just starting his collection currently owns five coins. These five coins consist of three fair coins with a head-on both faces, one fair coin with a head on one face and a tail on the other, and one biased coin with a head on one face and a tail on the other. when flipped, each fair coin has an equal probability of landing with a head or a tail on the upper face, whereas the biased coin has a probability of 0.65 of landing with a head on the upper face.

a. The collector randomly selects one of his five coins and flips it. What Is the probability that the upper face of the coin is a head? If the coin lands with a head on the upper face. what is the probability that the collector had selected the biased coin? If the coin lands with a head on the upper face. what is the probability that the lower face is a tail? Solve these three possibilities.

b. Suppose the collector repeated the process in part A eight times, i.e., each time he randomly selects one of the five coins and flips it. Among these eight flips, find the probability that the coin lands with a tail on the upper face more than two times The collector decides to throw away the coin he selected in part A. He then randomly selects one of the remaining four coins and flips

c. Suppose the coin the collector threw away was a fair coin with a head-on on both faces; Given this, find the probability that the newly selected coin lands with a head on the upper face.

d. Suppose the coin the collector threw away was the fair coin with a head on one face and a tail on the other. Given this, find the probability that the newly selected coin lands with a head on the upper face.

e. Suppose the coin the collector threw away was the biased coin with a head on one face and a tail on the other. Given this, find the probability that the newly selected coin lands with a head on the upper face. What about the probability that the newly selected coin lands with a tail on the upper face?