1.)In a family with 7 children what is the probability of having 6 boys and then 1 girl, in that order? (Exclude multiple births and assume all outcomes are equally likely).

Question

1.) 1.)In a family with 7 children what is the probability of having 6 boys and then 1 girl, in that order? (Exclude multiple births and assume all outcomes are equally likely).

2.)In a family with 7 children, what is the probability of having 6 boys and 1 girl, in any order? (Exclude multiple births and assume all outcomes are equally likely).

Answer 1

There are 2⁷ = 128 possible outcomes. This represent of having children with a possible combinations of boys and girls.

P(6 boys first, then 1 girl) = 1/128 = 0.0078125

The probability of having 6 boys first and then 1 girl is 0.0078125. There is only one possible combination that can work, which is BBBBBBG.

S = {BBBBBBG, BBBBBGB, BBBBGBB, BBBGBBB, BBGBBBB, BGBBBBB, GBBBBBB}

S is the sample space with possible combinations of 6 boys and 1 girl in any order.

P(6 boys and 1 girl) = 7/128 = 0.0546875

The probability of having 6 boys and 1 girl in any order is 0.0546875.