Question

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.

Answer 1

Answer:

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

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

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= {gggg}

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