APPLICATION

Expected Number Consider families with three children, and assume that the probability of having a girl is 1 2 .

(a) Complete the table for the probabilities of having 0, 1, 2, or 3 girls in a family of three children.

(b) Find the expected number of girls in a family of three children.

Number of girls	Probability
0	1 8
1
2
3

(a)

The table for the probabilities of having 0, 1, 2, or 3 girls in a family of three children.

Given:

The probability of having a girl is 12.

Approach:

The expression for probability is given as,

P=C(n,r)pr(1−p)n−r ...(1)

Here, P is the required probability and r successes in n independent trials of the experiment.

Calculation:

Calculate the probability of having 1 girl.

Substitute 12 for p, 1 for r and 3 for n in equation (1), to calculate the probability.

P(1)=C(3,1)(12)1(1−12)3−1=3(12)(14)=38

Calculate the probability of having 2 girl.

Substitute 12 for p, 2 for r and 3 for n in equation (1), to calculate the probability.

P(2)=C(3,2)(12)2(1−12)3−2=3(14)(12)=38

Calculate the probability of having 3 girl

(b)

The expected number of girls.