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I have some difficulties with following question.

A family has five children. Assuming that the probability of a girl on each birth was 1/2 and that the five births were independent, what is the probability the family has at least one girl, given they have at least one boy?

My solution is 1-(1/2)^4 = 15/16

However according to the book correct answer it 30/31.

Any ideas?

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