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## Official Guide Explanation:Problem Solving #160

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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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