## Probability

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### Probability

by swerve » Thu May 25, 2023 5:03 pm

00:00

A

B

C

D

E

## Global Stats

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]

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### Re: Probability

by Brent@GMATPrepNow » Fri May 26, 2023 5:57 pm
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
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