Three groups of children contain respectively 3 girls and 1 boy GMAT Problem Solving

Question: Three groups of children contain respectively 3 girls and 1 boy; 2 girls and 2 boys; 1 girl and 3 boys. One child is selected at random from each group. What is the probability that the three selected children consists of one girl and 2 boys?

1. \(\frac{7}{32}\)
2. \(\frac{9}{32}\)
3. \(\frac{11}{32}\)
4. \(\frac{13}{32}\)
5. \(\frac{15}{32}\)

Correct Answer: (D)

Solution and Explanation:

There is only one approach to this problem.

Approach Solution 1:

Since the question mentions that there are three groups, and also mentions that a child is selected from each group at random, we have 3 possible combinations in which the children are selected.

Let’s label the groups as Group A, Group B, Group C.

Combination 1: Girl (A), Boy (B), Boy (C)
Combination 2: Boy (A), Girl (B), Boy (C)
Combination 3: Boy (A), Boy (B), Girl (C)

Now for each combination, we need to calculate the individual probability for each independent event (selection of girl or boy from the respective group) and multiply them with each other to get a combined probability for that specific combination.

When we do that, we find:

Combination (1): P (Girl from A) * P (Boy from B) * P (Boy from C)

\(\frac{3}{4}*\frac{2}{4}*\frac{3}{4}=\frac{18}{64}\)
Combination (2): P (Boy from A) * P (Girl from B) * P (Boy from C)

\(\frac{1}{4}*\frac{2}{4}*\frac{3}{4}=\frac{6}{64}\)
Combination (3): P (Boy from A) * P (Boy from B) * P (Girl from C)

\(\frac{1}{4}*\frac{2}{4}*\frac{1}{4}=\frac{2}{64}\)

When we add the combined possibilities for Combination 1, 2, and 3, we get:

\(\frac{18}{64}*\frac{6}{64}*\frac{2}{64}=\frac{26}{64}=\frac{13}{32}\)

“Three groups of children contain respectively 3 girls and 1 boy; 2 girls and 2 boys; 1 girl and 3 boys. One child is selected at random from each group. What is the probability that the three selected children consists of one girl and 2 boys?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers assist the candidates to go through several sorts of questions that will enable them to enhance their mathematical understanding.

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