Question

Births Example 2 in this section includes the sample space for genders from three births. Identify the sample space for the genders from two births.

Short answer

The sample space for the genders resulting from two births is (bb, bg, gb, gg), where b represents a boy and g represents a girl.

Step-by-step solution

Given information

Genders from two births need to be listed in the form of a sample space.

Describe the sample space

The probability of an event is relative to sample space.

Sample space of an event is defined as the collection of all possible outcomes of that event.

In other words, a sample space has all the possible events of an experiment.

Identify the sample space

Assume there are two genders possible for the child—female and male.

Let b be the event that the child is male and g be the event that the child is female.

When two children are born, they follow the sequence of first birth and second birth.

Thus, for a series of two births, the following sample space shows the possible genders of the children:

$\text{Sample}\text{space =}\left(bb,bg,gb,gg\right)$

Here,

• bb represents both male births,
• bg represents the first male birth and second female birth,
• gb represents the first female birth and the second male birth, and
• gg represents both female births.