Question: 2 people are to be selected from Abraham, Benjamin, Chris, and Dave. What is the probability that both Abraham and Benjamin will be selected?

1. \(\frac{1}{12}\)
2. \(\frac{1}{6}\)
3. \(\frac{1}{3}\)
4. \(\frac{2}{3}\)
5. \(\frac{5}{6}\)

Solution with Explanation:
Approach Solution (1):

Probability of selecting Abraham =\(\frac{1}{4}\)

Probability of selecting Benjamin =\(\frac{1}{3}\)

Total probability =\(\frac{1}{4}\)*\(\frac{1}{3}\)because the sequence of selecting Abraham or Benjamin is not important!

Therefore, Probability =\(\frac{1}{12}\)

So the total probability of both Abraham and Benjamin is =\(\frac{1}{12}\)+\(\frac{1}{12}\)=\(\frac{1}{6}\)

Correct Option: B

Approach Solution (2):

First A and then B:

P (Abraham) =\(\frac{1}{4}\)

P (Benjamin) =\(\frac{1}{3}\)

P (both B and A) =\(\frac{1}{4}\)*\(\frac{1}{3}\)=\(\frac{1}{12}\)

First B and then A:

P (Benjamin) =\(\frac{1}{4}\)

P (Abraham) =\(\frac{1}{3}\)

P (both B and A) =\(\frac{1}{4}\)*\(\frac{1}{3}\)=\(\frac{1}{12}\)

Overall Probability =\(\frac{1}{12}\)+\(\frac{1}{12}\)=\(\frac{1}{6}\)

Correct Option: B

“2 people are to be selected from Abraham, Benjamin, Chris, and Dave. What is the probability that both Abraham and Benjamin will be selected?”- 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. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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