You are handed two coins, Coin S and Coin W. Coin S is a standard coin, with a 50% chance of turning up heads when it’s tossed. Coin W is a weighted coin with an 80% chance of turning up heads when it’s tossed. You choose one of the coins randomly and toss it twice. Draw a three-stage probability tree and use it to answer the following questions.
a. What is the probability that you toss two heads?
b. Before you toss the coin, there is a 50% probability that you selected the standard coin, Coin S. If you end up tossing two heads, how likely is it that the coin you are tossing is Coin S?
c. If your two tosses produce one head and one tail, how likely is it that you selected Coin S?