Find the sample space and probability

Question

A couple has three children.

i) Find the sample space for this experiment.

ii) Find the probability of getting at least one child of each gender.

Answer 1

Another sample space question.

Sample space is the set of all possible outcomes.

1) If gender of child (boy/girl) is the variable and the couple has 3 children, and we take into account birth order, then the outcomes are:

1. 3 boys (BBB)
2. 2 boys and 1 girl (BBG, BGB, or GBB)
3. 1 boy and 2 girls (GGB, GBG, or BGG)
4. 3 girls (GGG)

2) Find the probability of each. Three boys (or three girls) is easiest: 1/2 * 1/2 * 1/2 = 1/8. Alternately, we can just use the orders above and count. At least one child of each gender means NOT all boys and NOT all girls, or the two middle groups. 6/8.