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Suppose that a family wants to have four children. (Enter the probabilities as fractions.) (a) What is the sample space? (Let B represent a boy and G represent a girl. To indicate that the first child is a boy, the second child is a boy, the third child is a boy, and the fourth child is a girl enter BBBG. Enter your answers as a comma-separated list.)

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Answer: {BBBB , GGGG , BBBG , BBGB , BGBB , GBBB, BBGG,  GGBB , GBBG, BGGB ,BGBG , GBGB, BGGG, GBGG, GGBG , GGGB}

Step-by-step explanation:

A sample space is the total possible outcomes associated in a particular event.

For example : It we toss a fair coin that has two faces (Tail and Head), then the possible outcomes are T or H.

Thus , sample space will be S={T,H}  

If we toss two fair coins then the sample space will be :

S={TT, TH , HT, HH}

Given : A family wants to have four children.

The possible outcomes for a child : A girl or a boy

Let B represent a boy and G represent a girl.

Then , the possible outcomes for having four children:

BBBB , GGGG

BBBG , BBGB , BGBB , GBBB,

BBGG,  GGBB , GBBG, BGGB ,BGBG , GBGB,

BGGG, GBGG, GGBG , GGGB

Hence the required sample space : {BBBB , GGGG , BBBG , BBGB , BGBB , GBBB, BBGG,  GGBB , GBBG, BGGB ,BGBG , GBGB, BGGG, GBGG, GGBG , GGGB}

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