[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
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
A jar contains 4 balls, labeled 1,2,3, and 4. A ball is sel
This topic has expert replies
-
Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
P = (ways to draw 2 balls with a difference of 1)/(total ways to draw 2 balls).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
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
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!
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 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
=>
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
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
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7247
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
The following are favorable outcomes for the two draws:
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
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
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
