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If an unbiased coin is flipped 5 times, the probability that the same face does not show up in any three consecutive flip is?

If an unbiased coin is flipped 5 times, the probability that the same face does not show up in any three consecutive flip is? Correct Answer 1/2

Calculation:

⇒ When a coin flipped 5 times we have possible outcomes = 25 = 32

⇒ The favourable cases would arise when there are 4 heads, 1 tail; 3 heads, 2 tail; 2 heads, 3 tail; and 1 head, 4 tails.

⇒ In 4 heads 1 tail case, we have HHTHH as the only favourable sequences = 1

⇒ In 3 heads, 2 tails case, we have 10 cases in all of which HHHTT, TTHHH, THHHT are unfavourable sequences, thus we get favourable case = 7

⇒ Similarly, we can count 7 + 1 = 8 cases for 2 heads, 3 tails and 1 head, 4 tails.

⇒ Thus 16 cases are favourable out of 32

⇒ Thus the probability = 16/32 = 1/2

∴ The required result will be 1/2.

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