Three Children – A couple are planning to have 3 children. What is the sample space for three children? (What are all the possible outcomes for three children? Assume that boys and girls are equally likely, so that the sample events are equally likely.
3 b
2 b, 1 g
1 b, 2 g
3 g
so 4 possible outcomes, all equally likely
p of each is .25
To determine the sample space for three children, we need to consider all the possible outcomes for each child. Since each child can either be a boy or a girl, and we assume that boys and girls are equally likely, we have two possible outcomes for each child.
Let's label the possible outcomes as follows:
B - Boy
G - Girl
Now we can list all the possible combinations for three children, considering the order in which they were born:
1. BBB (All boys)
2. BBG (Two boys, one girl)
3. BGB (One boy, two girls)
4. BGG (One boy, two girls)
5. GBB (One girl, two boys)
6. GBG (One girl, two boys)
7. GGB (Two girls, one boy)
8. GGG (All girls)
Therefore, the sample space for three children consists of these eight possible outcomes:
{BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}