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A coin is tossed 3 times. What is the probability that the tosses are the same?
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There are $2^3=8$ possible outcomes after tossing a fair coin fairly 3 times. The 8 possible outcomes are: TTT, HTT, THT, TTH, HHT, HTH, THH, HHH. Exactly 2 of 8 possible outcomes result in $\mathbf{3}$ of the same faces showing up. They are TTT and HHH. Each has a probability of $\dfrac{1}{8}$ of happening and since either showing up satisfactorily addresses the criterion for success, the probability as requested $=2 \times (\dfrac{1}{8})=\dfrac{1}{4}=.25$ $=25 \%$.
by Diamond (74,795 points)

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