The Patterson family has 3 kids, 1 boy and 2 girls.

Question

Suppose that for each birth, the probability of a boy birth is 1/2, and the probability of a girl birth is also 1/2. What is the fractional probability of having 1 boy and 2 girls, in any order, in a family's first 3 births?

Answer 1

To calculate the fractional probability of having 1 boy and 2 girls in a family's first 3 births, we need to consider all the possible outcomes.

There are 3 possible ways to have 1 boy and 2 girls in a family's first 3 births:
1. BGG
2. GBG
3. GGB

Each birth is an independent event, so we can calculate the probability of each of these outcomes separately.

The probability of having a boy followed by 2 girls is:
(1/2) * (1/2) * (1/2) = 1/8

Since there are 3 ways to have 1 boy and 2 girls, we multiply the probability of each outcome by 3.
Fractional probability = 3 * (1/8) = 3/8

Therefore, the fractional probability of having 1 boy and 2 girls in any order in a family's first 3 births is 3/8.