A jar contains 4 balls, labeled 1,2,3, and 4. A ball is sel

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Mon Apr 09, 2018 1:23 am

[GMAT math practice question]

A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from the jar, and its number is recorded before it is returned to the jar. If a second ball is then selected from the jar, what is the probability that the difference between the numbers on the two balls selected is 1?

A. 1/3
B. 3/4
C. 1/2
D. 5/8
E. 3/8

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Apr 09, 2018 2:18 am

Max@Math Revolution wrote:[GMAT math practice question]

A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from the jar, and its number is recorded before it is returned to the jar. If a second ball is then selected from the jar, what is the probability that the difference between the numbers on the two balls selected is 1?

A. 1/3
B. 3/4
C. 1/2
D. 5/8
E. 3/8

P = (ways to draw 2 balls with a difference of 1)/(total ways to draw 2 balls).

Total ways to draw 2 balls:
Number of options for the first ball = 4. (Any of the 4 numbers.)
Number of options for the second ball = 4. (Any of the 4 numbers.)
To combine these options, we multiply:
4*4 = 16.

Ways to draw 2 balls with a difference of 1:
1,2
2,1
2,3
3,2
3,4
4,3
6 options.

Thus:
P = 6/16 = 3/8.

The correct answer is E.

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swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Mon Apr 09, 2018 9:56 am

Way you can choose first ball - 4 ways

Next ball - 4 ways again as ball has been returned

ways - 4 * 4 = 16

Ways in which difference is 1:

A) If the first ball is 2 or 3, next ball can be picked in TWO ways
2 . . . . . 2 or 3
3 . . . . . 2 or 4
So, 2 * 2 = 4 ways.

B) But if the first ball is 1 or 4, next ball can be picked in ONE way
1 . . . . . only 2
2 . . . . . only 4
So, 1 * 2 = 2 ways.

Total 2*2 + 2*1 = 6

Probability = 6/16 = 3/8. Option E.

Regards!

Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Wed Apr 11, 2018 4:44 am

=>

The total number of ways the two balls may be selected is 4C2 = ( 4 * 3 ) / ( 1 * 2 ) = 6.
There are three ways in which the numbers on the two balls selected can have a difference of 1: ( 1, 2 ), ( 2, 3 ), and ( 3, 4 ).

Thus, the probability is 3/6 or 1/2

Therefore, C is the answer.
Answer: C

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

hi

by Scott@TargetTestPrep » Wed Apr 11, 2018 5:45 am

A jar contains 4 balls, labeled 1,2,3, and 4. A ball is selected from the jar, and its number is recorded before it is returned to the jar. If a second ball is then selected from the jar, what is the probability that the difference between the numbers on the two balls selected is 1?

A. 1/3
B. 3/4
C. 1/2
D. 5/8
E. 3/8

The following are favorable outcomes for the two draws:

1, 2

2, 1

3, 2

2, 3

3, 4

4, 3

We see that we have 6 favorable outcomes. The total number of outcomes is 4 x 4 = 16, since there are always 4 balls in the jar for each of the two picks.

P(that the difference between the numbers on the two balls selected is 1) = 6/16 = 3/8.

Answer: E

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