Suppose you believe that on the first toss a coin is equally likely to come up heads or tails. You also believe that the first toss and the second toss are relevant to each other: depending on the...

Suppose you believe that on the first toss a coin is equally likely to come up heads or tails. You also believe that the first toss and the second toss are relevant to each other: depending on the outcome of the first toss, you have different probabilities for the outcome of the second toss.

a. Represent this situation with a relevance diagram.

b. Suppose you believe that if the first toss is a head, the chance of getting a head on the second toss is 3/4 and of getting a tail is 1 /4. If, the first toss is a tail, then the chance of getting a head on the second toss is 1/4 and of getting a tail is 3/4.

c. Draw a probability tree to represent this information, filling in all probabilities.

d. From the tree, determine the probabilities of getting two heads; a head followed by a tail; and exactly one head in two tosses.