QUESTION 3 - Probability [20 marks] Tom is a baseball player who is easily injured during the match. When Tom is playing, the probability that Tom' team will win is 4/5 , but otherwise it is only 1/2. The probability that Tom will be fit to play in a match this weekend is 2/3. (a) Draw a probability tree to summarise this information and find the probability of each outcome. What is the probability that Tom's team will win this weekend's match? [8 marks] (b) Suppose that Tom' team do win this weekend's match. Flip your probability tree from part (a). Hence, find the probability that Tom was not fit to play in the match. [6 marks] (c) Suppose that when Tom plays in a match, he scores one goal with probability 1/4, two goals with probability 1/8, and otherwise scores no goals. Consider Tom plays 20 matches, how many goals would Tom be expected to score? In addition, how many matches that Tom expected to score no goals? [6 marks]