Official Guide Explanation:
Problem Solving #160

Background

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Solution and Metadata

Question: 160
Page: 83
Difficulty: 7 (Very Difficult)
Category 1: Arithmetic > Discrete Probability >
Category 2: Word Problems > Other >

Explanation: It may be easier to consider all of the other probabilities.

The odds of having four boys are ((1/2))⁴ = (1/16)

The odds of having four girls are the same.

The odds of having exactly one boy consider the four ways of doing so:

B G G G

G B G G

G G B G

G G G B

The odds of any one of those happening is (1/16), and since there are four of them, the odds of having exactly one boy are 4((1/16)) = (4/16) = (1/4)

The odds of having exactly one girl are the same.

Thus, all of the possibilities EXCEPT for having two boys and two girls are:

(1/16) + (1/16) + (1/4) + (1/4) = (10/16) = (5/8)

What's left over, meaning the probability of having two boys and two girls, is:

1 - (5/8) = (3/8), choice (A).

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