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## Main Question or Discussion Point

Can anyone explain to me how this problem is solved

Determine the probability that the first head appears on an odd number of flips i.e. X contains {1,3,5..}.

P[X] = summation starting at x = 1 to infinity (1/2)^(2x-1) = 1/2 / (1 - 1/4) = 2/3

Basically my question is, how is the formula for P[X] obtained:

1. 1/2 / (1 - 1/4) : where does this come from?

2. summation starting at x = 1 to infinity (1/2)^(2x-1) and this as well

Determine the probability that the first head appears on an odd number of flips i.e. X contains {1,3,5..}.

P[X] = summation starting at x = 1 to infinity (1/2)^(2x-1) = 1/2 / (1 - 1/4) = 2/3

Basically my question is, how is the formula for P[X] obtained:

1. 1/2 / (1 - 1/4) : where does this come from?

2. summation starting at x = 1 to infinity (1/2)^(2x-1) and this as well