Suppose there are three children in a family. The tree diagram represents the order in which the children may have been born in relation to their gender. How many outcomes are in this sample space?
Responses
A 2
B 3
C 4
D 8
The tree diagram for the order in which the children may have been born in relation to their gender would look like this:
Gender 1
|
------------------
| | |
Gender 2 Gender 2 Gender 2
| | |
--------- ----------- ---------
| | | | | | | | |
G B B G G B B G G B B G
There are two possibilities for the gender of the first child (either boy or girl), and for each gender choice, there are two possibilities for the gender of the second child. Therefore, there are 2 x 2 = 4 possibilities for the gender of the first two children. For each of these possibilities, there are again two possibilities for the gender of the third child. Therefore, the total number of outcomes in this sample space is 4 x 2 = 8.
So, the answer is D) 8.