Suppose that a family has four children What is the probabil

Suppose that a family has four children. What is the probability that at least two are female?

a. 1/2

b. 5/16

c. 11/16

d. 9/16

e. 10/16

Solution

Let G shows the event that child is Girl and B shows the event that child is a Boy. So

P(G)=P(B)= 1/2=0.5

Sample space of a family of four children will be

S= {BBBB, BBGB, BBBG. BGBB, GBBB, BBGG, BGGB, GGBB, GBBG, BGBG, GBGB, BGGG, GBGG, GGBG, GGGB, GGGG}

Out of 16 possible outcomes, there are 11 outcomes which has atleast 2 female. So the probability that at least two are female will be

P( at least two female) = 11/16

hence, option c is correct.