A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The 8 outcomes are listed in the table below. Note that each outcome has the same probability.For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.Outcomes ProbabilityTTH HTH HHH HTT HHT TTT THT THHEvent A: Alternating tail and head (with either coming first) Event B: A tail on the first toss or the third toss (or both) Event C: Exactly one head
Question
A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The 8 outcomes are listed in the table below. Note that each outcome has the same probability.For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.Outcomes ProbabilityTTH HTH HHH HTT HHT TTT THT THHEvent A: Alternating tail and head (with either coming first) Event B: A tail on the first toss or the third toss (or both) Event C: Exactly one head
Solution
The outcomes of the coin tosses are: TTH, HTH, HHH, HTT, HHT, TTT, THT, THH.
Event A: Alternating tail and head (with either coming first) The outcomes that fit this description are: HTH, THT. So, the probability of this event is 2/8 = 1/4.
Event B: A tail on the first toss or the third toss (or both) The outcomes that fit this description are: TTH, HTT, TTT, THT. So, the probability of this event is 4/8 = 1/2.
Event C: Exactly one head The outcomes that fit this description are: TTH, HTT, THT. So, the probability of this event is 3/8.
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