The probability that no two consecutive flips have the same result is [tex]\frac{1}{16}[/tex].
If a coin is flipped then there are two possible outcomes Head(H) and Tail (T).
So each flip can have 2 possible outcomes. It means 5 flips have [tex]2^5=32[/tex] possible outcomes.
Among these 32 outcomes only 2 outcomes : HTHTH and THTHT have "no two consecutive flips have the same result".
So the probability that no two consecutive flips have the same result is = [tex]\frac{2}{32} =\frac{1}{16}[/tex].
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