In: Statistics and Probability
In a family of 4 children, what is the probability that two of the children are boys and two of the children are girls? |
answer correct to 4 decimal places
Solution:
Given: a family of 4 children is selected.
Thus sample space S is:
4 Boys | 3 Boy 1 Girl | 2 Boys 2 Girls | 1 Boy 3 Girls | 4 Girls |
---|---|---|---|---|
BBBB | BBBG | BBGG | BGGG | GGGG |
BBGB | BGBG | GBGG | ||
BGBB | GBBG | GGBG | ||
GBBB | GBGB | GGGB | ||
GGBB | ||||
BGGB |
We have to find:
P( two of the children are boys and two of the children are girls) =.............?
That is:
P( 2 Boys and 2 Girls) = ..............?
From above table, we have n = total outcomes in sample space = 16
and m = number of outcomes of 2 Boys and 2 Girls = 6
thus
P( 2 Boys and 2 Girls) = m / n
P( 2 Boys and 2 Girls) = 6 / 16
P( 2 Boys and 2 Girls) = 3 / 8
P( 2 Boys and 2 Girls) = 0.3750