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A coin is flipped until a head appears. What is the probability that a head appears...

A coin is flipped until a head appears. What is the probability that a head appears on an odd-numbered flip?

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Answer #1

The probability that a head appears on an odd-numbered flip is

This is a geometric series that sums to be a / 1 - r where a is first term i.e. 1/2, r is the geometric ratio i.e. 1/4

The required probability is (1/2) / [1 - (1/4)] = (1/2) / (3/4) = 2/3

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