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 possibility that the 2 apples selected will include the spoiled apple?

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 possibility 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

GMAT tutoring students tend to dislike probability questions. A couple of things to remember regarding GMAT probability:

  1. It doesn’t come up that much.
  2. When it does come up often the question isn’t that challenging.
  3. If you do get a challenging probability question you can always skip.

Let’s focus on the question first: what is the possibility that the 2 apples selected will include the spoiled apple?

We need a spoiled apple selected. OK. There’s a very practical way of doing this:

G1 G2 G3 G4 S

10 Possible pairs. 4 of them have a spoiled apple. So 4/10 or 2/5 chance of having a pair with the spoiled apple.

G1 G2

G1 G3

G1 G4

G1 S

G2 G3

G2 G4

G S

G3 G4

G3 S

G4 S

Easy. If the numbers are small there’s nothing wrong with writing things out. In fact, it can be the best approach.

The other way to do it is with the slot method. Calculate the number of ways to create a group of two from 5 things. That will be your total or your denominator. And then calculate the number ways to create a group of two with the constraint that one of those things (the spoiled apple) must be included. That will be your numerator. Remember that probability is just specific scenario/all scenarios.

5*4/1*2 = 10 (the number of ways to create a pair from 5 things)

With one of the spots reserved for the spoiled apple you’re only left with the other spot to populate. So how many things can go in that spot? 4 (the 4 good apples). So the numerator is 4 and the denominator is 10. 4/10 = 2/5.

More Challenging GMAT Combinatorics/Probability Examples

Here’s an even more challenging GMAT Combinatorics/Probability question with an in depth explanation:

Tanya prepared 4 different letters to be sent to 4 different addresses.

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