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).