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 ProbabilityTHH TTT HTT HHH TTH HHT HTH THTEvent A: No heads on the first two tosses Event B: A tail on the second toss Event C: Alternating head and tail (with either coming first)
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 ProbabilityTHH TTT HTT HHH TTH HHT HTH THTEvent A: No heads on the first two tosses Event B: A tail on the second toss Event C: Alternating head and tail (with either coming first)
Solution
The outcomes and their probabilities are as follows:
- THH - Probability: 1/8
- TTT - Probability: 1/8
- HTT - Probability: 1/8
- HHH - Probability: 1/8
- TTH - Probability: 1/8
- HHT - Probability: 1/8
- HTH - Probability: 1/8
- THT - Probability: 1/8
Event A: No heads on the first two tosses. The outcomes that satisfy this condition are TTT and TTH. So, the probability of Event A is 2/8 or 1/4.
Event B: A tail on the second toss. The outcomes that satisfy this condition are TTH, TTT, HTH, and HTT. So, the probability of Event B is 4/8 or 1/2.
Event C: Alternating head and tail (with either coming first). The outcomes that satisfy this condition are THH, HTH, and THT. So, the probability of Event C is 3/8.
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