Five multiple choice questions

1. A coin is tossed 4 times. We use H to denote heads and T to denote tails. For instance, HTHH means we got the sequence heads, tails, heads, heads.
(a) Write down the elements of the sample space. Hint: Using a tree diagram can be helpful. (b) List the outcomes included in each of the following events. Also compute the probabilities for each event. Assume that the coin is fair. • Event A: Number of times the coin came up heads is 0. • Event B: Number of times the coin came up heads is 1. • Event C: The first two tosses came up heads. • Event D: Number of times the coin came up heads is greater than 1. (c) Answer YES or NO to the following questions: • Are the events A and B mutually exclusive? • Are the events B and C mutually exclusive? • Are the events C and D mutually exclusive? (d) Compute the probability P(A∪D). (e) Compute the probability P(C ∪D).