Suppose that a coin is tossed three times and the side showing face up on each toss is noted. Suppose also that on each toss heads and tails are equally likely. Let HHT indicate the outcome heads on the first two tosses and tails on the third, THT the outcome tails on the first and third tosses and heads on the second, and so forth. A) Use set-roster notation to describe the elements in the sample space whose outcomes are all the possible head-tail sequences obtained in the three tosses.
B) Write each of the following events as a set and find its probability:
(i) The event that exactly one toss results in a head.
(ii) The event that at least two tosses result in a head.
(iii) The event that no head is obtained.