In a family with 6 children, let success be defined as having a baby girl, and find the probability that the first girl is the first child born. The First Girl is the 2nd or 4th child born. The first girl is the last child born. There are no girls born into this family.
Assuming that the baby girl or equally likely, the probability of having a baby girl = 0.5
Probability that the first girl is the first child born = 0.5
Probability that the first Girl is the 2nd or 4th child born = Probability that the first Girl is the 2nd child + Probability that the first Girl is the 4th child born
= Probability that the first child is boy followed by a girl + Probability that the first three children were boys followed by a girl
= 0.5 * 0.5 + 0.53 * 0.5
= 0.3125
Probability that first girl is the last child born = Probability that the first five children were boys followed by a girl
= 0.55 * 0.5
= 0.015625
Probability that there are no girls born into this family = Probability that all 6 children were boys
= 0.56 = 0.015625
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