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An urn contains 10 balls, numbered from 1 to 10. If 2 balls

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An urn contains 10 balls, numbered from 1 to 10. If 2 balls

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Source: Veritas Prep

An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what is the probability that the sum of the 2 numbers on the balls will be even?

A. 25%
B. 37.5%
C. 50%
D. 62.5%
E. 75%

The OA is C

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BTGmoderatorLU wrote:
Source: Veritas Prep

An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what is the probability that the sum of the 2 numbers on the balls will be even?

A. 25%
B. 37.5%
C. 50%
D. 62.5%
E. 75%
There are exactly 4 equiprobable events:

E1 = first ball odd , second ball odd
E2 = first ball odd, second ball even
E3 = first ball even, second ball odd
E4 = first ball even, second ball even

Exactly two of the 4 events mentioned above are favorable (E1 and E4), hence the correct answer is 50% (C).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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GMAT/MBA Expert

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Hi All,

We're told that an urn contains 10 balls, numbered from 1 to 10 and we're told that 2 balls are selected at random WITH replacement. We're asked for the probability that the SUM of the 2 numbers on the balls will be EVEN. This question can be solved in a couple of different ways, including as a straight-probability question.

To start, there are two ways to get a sum that is EVEN:

(Odd on the first) and (Odd on the second)
(Even on the first) and (Even on the second)

Since there are an equal number of Odd and Even numbers AND we are replacing the first ball before we pull the second, the probability of pulling one Odd or one Even is the same each time: 1/2

(Odd) and (Odd) = (1/2)(1/2) = 1/4
(Even) and (Even) = (1/2)(1/2) = 1/4
Total probability of ending with a sum that is Even on two balls is 1/4 + 1/4 = 2/4 = 1/2

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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There are 10 balls; 5 of which are even and 5 of which are odd.

Probability of drawing 1 even ball is 50%
Probability of drawing 1 odd ball is 50%

Here are the possible combos:
1. Draw even; Draw Even ==> Adds to Even
2. Draw odd; draw odd ==> adds to even

For (1): 50% * 50%
For (2): 50% * 50%

Then add them up, 25% + 25% = 50%

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