Question

An experiment consists of recording boy-girl composition of families with 2 children.
a) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?
b) What is the sample space if we are interested in the number of girls in the family?

Answer 1

Hint: Here, the families will have two children and we have to calculate the possibilities of the occurrence of either boy or girl in the order of their births. So in this, we just need to pair all the possibilities that can occur. Similarly for the sample space, the idea will be the same.

Complete step-by-step answer:

As the family has two children. So, they can be both boys, both girls or 1 boy and 1 girl.

Here, we will have to consider the occurrence of births also. For example if the first baby is boy and the second baby is girl, the possibility is {boy, girl} and in case, the first baby is girl and the second baby is boy, that will be a different possibility. So the sample space when we consider the order of birth of a boy or girl is

$\{ $

(Boy, Girl),

(Boy, Boy),

(Girl, Boy),

(Girl, Girl)

$\} $

Since, the maximum number of children in a family is 2, and we are considering only girls in a family, then a family can have 0, 1 or 2 girls.

So, the sample space of the number of girls in a family is
$\{ 0,1,2\} $

Note: The thing that we should notice here is the difference between sample space and an event. The set of all the possible outcomes is called the sample space of the experiment and is usually denoted by S. Any subset E of the sample space S is called an event.