Question

a couple decides to have children until they have one boy and one girl, but they will not have more than three children. choose the correct sample space for this random experiment.

os = {ggg, ggb, gbg, gbb, bbb, bbg, bgb, bgg}
os = {ggg, ggb, bbb, bgg}
os = {gb, bg, bbg, ggb}
os = {gb, bg, bbg, ggb, bbb, ggg}

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Explanation:

Step1: Analyze first - two - child cases

If the first two children are of different genders, the couple stops. So, GB (girl then boy) and BG (boy then girl) are part of the sample space.

Step2: Analyze cases where first two are same - gender

If the first two are girls (GG), they have a third child. If the third is a boy, the sequence is GGB. If the first two are boys (BB), they have a third child. If the third is a girl, the sequence is BBG.

Step3: Analyze cases of three - same - gender children

The couple will stop after three children even if they don't have both genders. So, BBB and GGG are also in the sample space as they are valid end - points within the three - child limit.

Answer:

S = {GB, BG, BBG, GGB, BBB, GGG}