Question

Four children were born at City Hospital yesterday. Assume each child is equally likely to be a boy or a girl. Which of the following outcomes is most likely?

all $4$ are boys

all $4$ are girls

$2$ are girls and $2$ are boys

$3$ are of one gender and $1$ is of the other gender

all of these outcomes are equally likely

Solution:

There are $2^4=16$ equally likely birth-order outcomes. The counts by category are: all boys, $1$ ; all girls, $1$ ; two boys and two girls, $\binom{4}{2}=6$ ; and three of one gender and one of the other, $2\binom{4}{1}=8$ .

The largest count is $8$ , so the most likely outcome is three children of one gender and one of the other.

Thus, D is the correct answer.

2014 AMC 8 Problem 18

Solution:

Problem 18 in Other Years