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
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
An urn contains 10 balls, numbered from 1 to 10. If 2 balls
This topic has expert replies
-
BTGmoderatorLU
- Moderator
- Posts: 2209
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
-
fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
There are exactly 4 equiprobable events: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%
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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
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
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%
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%
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7245
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
The sum of the 2 numbers will be even if the 2 numbers chosen are both even or both odd. The probability of choosing 2 even numbers is 1/2 x 1/2 = 1/4. Likewise, the probability of choosing 2 odd numbers is 1/2 x 1/2 = 1/4. Therefore, the probability of choosing 2 numbers whose sum is even is 1/4 + 1/4 = 1/2.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%
The OA is C
Answer: C
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
