Question

An experiment consists of recording, in order of their births, the sex composition of a four-child family in which the children were born at different times. (Let b represent the birth of a boy and g represent the birth of a girl. Enter your answers using letter combinations separated by commas. Example: bgbg, gggg, ...)

(a) Describe an appropriate sample space S for this experiment.
(b) Describe the event E that there are three boys and a girl in the family.

Answer 1

(a) An appropriate sample space S for this experiment is the set of all possible sequences of four children, where each child can be either a boy (b) or a girl (g). So, the sample space S is:

S = {bbbb, bbbg, bbgb, bgbb, gbbb, bggg, bgbg, gbgg, ggbb, gbgb, bggg, gbgg, gggg, gggb, gggg}

There are 2^4 = 16 possible outcomes in the sample space.

(b) The event E that there are three boys and a girl in the family can be represented by the set of all sequences in the sample space S that have three b's and one g. So, the event E is:

E = {bbbg, bbgb, bgbb, gbbb}

There are 4 possible outcomes in the event E.