A family has 4 children Write its sample space and find the

A family has 4 children. Write its sample space and find the following probabilities: (A) Having no more than 2 boys. (B) Having no boys. (C) Having exactly 2 girls.

Solution

Sample space = (GGGG, GGGB, GGBG,GBGG,BGGG,GGBB,BBGG,GBGB,BGBG,GBBG,BGGB,GBBB,BGBB,BBGB,BBBG,BBBB)

Now From this sample space only
P(no nore than 2 boys ) = P(0 boy) + P(1boy) + P (2boy) = 11/16(ans)

P (no boy ) = 1/16(ans)

P( 2 girls) = 6/16 = 3/8 (ans)