Question

A couple plans to have two children. Each child is equally likely to be a girl or​ boy, with gender independent of that of the other child. a. Construct a sample space for the genders of the​ children, using B for boy and G for girl. b. Find the probability that both of the children are girls. c. Answer part b​ if, in​ reality, for a given​ child, the chance of a girl is 0.48.

Answer 1

a)

G - G

G - B

B - B

B - G

b) 25% probability that both of the children are girls.

c) 23.04% probability that both of the children are girls.

Explanation:

a. Construct a sample space for the genders of the​ children, using B for boy and G for girl.

B for boy

G for girl

Each child can be a boy or a girl

Two children

First child - Second child

G - G

G - B

B - B

B - G

b. Find the probability that both of the children are girls.

Two children

Each has a 50% probability of being a girl

So

0.5*0.5 = 0.25

25% probability that both of the children are girls.

c. Answer part b​ if, in​ reality, for a given​ child, the chance of a girl is 0.48.

Two children

Each has a 48% probability of being a girl

So

0.48*0.48 = 0.2304

23.04% probability that both of the children are girls.