Consider the composition of a three-child family. Assume that a girl is as likely as a boy at each birth. What is the probability that there is one boy and two girls in the family?
I believe the answer is 3/8.
3/8 is correct.
It can be calculated as follows:
A. By enumeration
GGG
GGB
GBG
BGG
BBG
BGB
GBB
BBB
So out of the 8 possible combinations, there there are 3 (second to fourth) that have two girls and 1 boy.
B. By enumeration, useful for large numbers.
number of possible combinations = 2³
Note: B or G are the 2 possible outcomes, and there are 3 children.
Number of possible combinations of 2 girls and 1 boy (out of 3 children
= 3!/(2!1!)
= 3*2*1/(2*1 * 1)
= 3
So probability = 3/8
To determine the probability of having one boy and two girls in a three-child family, we need to consider all the possible combinations of boys and girls.
Let's assign the letter "B" for a boy and "G" for a girl.
Possible outcomes:
1. BGG (boy, girl, girl)
2. GBG (girl, boy, girl)
3. GGB (girl, girl, boy)
These are the three possible combinations where there is exactly one boy and two girls.
Since each birth has an equal probability of being a boy or a girl (1/2), we can calculate the probability of each outcome by multiplying the probabilities together.
Probability of BGG: (1/2) * (1/2) * (1/2) = 1/8
Probability of GBG: (1/2) * (1/2) * (1/2) = 1/8
Probability of GGB: (1/2) * (1/2) * (1/2) = 1/8
Adding up the probabilities of these three outcomes, we get:
Probability of having one boy and two girls = 1/8 + 1/8 + 1/8 = 3/8
Therefore, the probability of having one boy and two girls in a three-child family is 3/8.