# Suppose a couple has three children. Assume the likelihood of having a boy or a girl is the same. a. What is the sample space? b. What is the probability that all the children are boys? c. If you...

Suppose a couple has three children. Assume the likelihood of having a boy or a

girl is the same.

a. What is the sample space?

b. What is the probability that all the children are boys?

c. If you know two of the children are boys, does it change the sample

space? Explain.

### 1 Answer | Add Yours

(a) Let **B** represent Boy and **G** represent girl .

There are total three children.

So possible sample space is

**S={ BBB ,BBG,BGB,GBB,BGG,GBG,GGB,GGG }**

BBB - all children are boy.Similarly you can define other

(b)

no of possible out comes =8

elements of sample space.

E= all boys

E={ **BBB** }

no. of favourable out come= 1

element in E

P(E)= no.(E)/no.(S)

=1/8

(c) If we know amongs three children ,two are boy then sample space is

**S'={BBG,BGB,GBB }**

**sample space change.**