The sample space listing the eight simple events that are possible when a couple has three children is {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. After identifying the sample space for a couple having four children, find the probability of getting four girls and no boys. Identify the sample space for a couple having four children.

S= {, bbgb, bgbb, bggb, gbbb, gbgb, ggbb, gggb,bbbg, bbgg, bgbg, bggg, gbbg, gbgg, ggbg, }

P( getting four girls and no boys)=0.0625

Step-by-step explanation:

The sample space for having four children can be written as

Sample space=S= {, bbgb, bgbb, bggb, gbbb, gbgb, ggbb, gggb,bbbg, bbgg, bgbg, bggg, gbbg, gbgg, ggbg, }

where b stands for boy and g stands for girl.

number of elements in sample space=n(S)=16

P( getting four girls and no boys)=?

getting four girls and no boys= {}

n( getting four girls and no boys)=1

P( getting four girls and no boys)=n( getting four girls and no boys)/n(S)

P( getting four girls and no boys)=1/16

P( getting four girls and no boys)=0.0625