Question

In: Statistics and Probability

In a family of 4 children, what is the probability that two of the children are...

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

Solutions

Expert Solution

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

orchestra answered 1 year ago
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