Question

A family has three children. An outcome is represented by a string GBB (meaning the oldest child is a girl, the second oldest is a boy, and the youngest is a boy).

Find the probability of:

i) A girl on the first birth.
ii) Exactly two boys.
iii) First child and third child are both girls.

Answer 1

The probability of a girl on the first birth is 1/2, the probability of exactly two boys is 3/8, and the probability that the first child and third child are both girls is 1/4.

Step-by-step explanation:

To find the probability of different outcomes in a family with three children, we need to consider the sample space of all possible outcomes. Each child can be either a girl (G) or a boy (B). The sample space consists of 2^3 = 8 outcomes:

1. GGG
2. GGB
3. GBG
4. GBB
5. BGG
6. BGB
7. BBG
8. BBB

i) The probability of a girl on the first birth is 4/8 = 1/2, since there are 4 outcomes where the first child is a girl (GGG, GGB, GBG, GBB) out of 8 total outcomes.

ii) The probability of exactly two boys is 3/8, since there are 3 outcomes with exactly two boys (BGG, BGB, BBG) out of 8 total outcomes.

iii) The probability that the first child and third child are both girls is 2/8 = 1/4, since there are 2 outcomes where the first child and third child are both girls (GGG, GGB) out of 8 total outcomes.