Question: What is the probability for a family with three children to have a boy and two girls (assuming the probability of having a boy or a girl is equal)?

1. 1/8
2. 1/4
3. 1/2
4. 3/8
5. 5/8

Correct Answer: D
Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

• Assume the probability of having a boy or a girl is equal.

Find out:

• The probability for a family with three children to have a boy and two girls.

Probability(1B,2G) can be considered as either the choice of having exactly 1B and 2G or the total number of possibilities of sexes for 3 children.

Let’s assume Girls as G and Boys as B.

3 children can have certain possibilities of sexes such as:
GGG - three girls
GGB - two girls one boy
GBG- two girls one boy
GBB- two boys one girl
BGG-one boy two girls
BGB- two boys one girl
BBG- two boys one girl
BBB- three boys

Total possibilities of both sexes = 8

The number of choices where there are exactly 2 girls and 1 boy are:
GGB
GBG
BGG
=3.

Therefore, the probability for a family with three children to have a boy and two girls = 3/8

Approach Solution 2:
The problem statement informs that:

Given:

• Assume the probability of having a boy or a girl is equal.

Find out:

• The probability for a family with three children to have a boy and two girls.

The total number of possible sexes for 3 children = (Number of possible sex for each child)^(Number of children)
Number of possible sex for each child = 2 = (Boy or Girl)
Number of children = 3

Total possible sexes = 2^3 = 8

Possibilities to have exactly 2 Girls out of 3 children and 1 Boy out of the remaining 1 Child:
= 3C2 * 1C1 = 3

Therefore, the probability for a family with three children to have a boy and two girls = Favorable/total outcomes = 3/8.

Approach Solution 3:

The problem statement declares that:

Given:

• Assume the probability of having a boy or a girl is equal.

Find out:

• The probability for a family with three children to have a boy and two girls.

To determine the probability of a family with three children, two girls and one boy, this method will serve as an easier approach.
P(G-G-B) = 1/2 x 1/2 x 1/2 = 1/8

We also see that there are 3 ways to arrange two girls and one boy:
G-G-B
G-B-G
B-G-G

Therefore, the probability for a family with three children to have a boy and two girls = 1/8 x 3 = 3/8.

“What is the probability for a family with three children to have a boy”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “501 GMAT Questions”. GMAT Problem Solving questions enable the candidates to improve their skills in calculations in order to crack numerical problems. GMAT Quant practice papers assist the candidates to get familiar with several sorts of questions that will enable them to score better marks in the GMAT exam.

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