swerve wrote: ↑

Thu May 25, 2023 5:03 pm

A basket contains \(5\) apples, of which \(1\) is spoiled and the rest are good. If Henry is to select \(2\) apples from the basket simultaneously and at random, what is the probability that the \(2\) apples selected will include the spoiled apple?

A. \(1/5\)

B. \(3/10\)

C. \(2/5\)

D. \(1/2\)

E. \(3/5\)

The OA is C

[spoiler]Source: GMAT Prep[/spoiler]

Since there are so few objects involved (5 apples), we should be able to quickly answer the question by simply listing and counting

Let A, B, C, D, and E represent the 5 apples, and let E represent the SPOILED APPLE

We want to select 2 apples at random. So, let's list all of the possible outcomes:
1) AB
2) AC
3) AD
4) AE
5) BC
6) BD
7) BE
8) CD
9) CE
10) DE

So, there are 10 possible outcomes
Of those 10 possible outcomes, 4 outcomes include the SPOILED APPLE

So, P(selection includes the spoiled apple) = 4/10 = 2/5

Answer: C