BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

DS Questions on probability

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pm
Thanked: 114 times
Followed by:11 members

DS Questions on probability

by knight247 » Tue Jun 21, 2011 11:28 pm
There are 12 balls in an urn, out of which 4 balls are picked up at random. Is the probability
of all the four balls being red greater than 1/33 ?
(1)If two balls are picked up, the probability of both being red is 5/33
(2)There are 7 blue balls.
(A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
(B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
(C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
(D)EACH statement ALONE is sufficient to answer the question asked.
(E)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Wed Jun 22, 2011 12:13 am
knight247 wrote:There are 12 balls in an urn, out of which 4 balls are picked up at random. Is the probability of all the four balls being red greater than 1/33 ?
(1)If two balls are picked up, the probability of both being red is 5/33
(2)There are 7 blue balls.
Statement 1: From this information we can calculate the number of red balls and hence we can determine whether the required probability is greater than 1/33 or not.

Sufficient

Statement 2: As there are 7 blue balls, there are (12 - 7) = 5 red balls at max.
Hence, maximum required probability = (5/12)*(4/11)*(3/10)*(2/9) = 1/99
As the maximum probability is less than 1/99, the required probability will be always less than 1/99

Sufficient

The correct answer is D.

In case anyone has doubt with the explanation in statement 1:
  • Say, the number of red balls in the urn = n
    Hence, the probability of the first ball being red = n/12
    And, the probability of the second ball being red = (n - 1)/11

    So, (n/12)*((n - 1)/11) = 5/33
    --> n(n - 1) = 20
    --> n = 5

    Now we can calculate the probability of first four balls being red and we can compare that with 1/33.
Last edited by Anurag@Gurome on Wed Jun 22, 2011 12:49 am, edited 1 time in total.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Wed Jun 22, 2011 12:41 am
Anurag@Gurome wrote:

Statement 2: Doesn't provide any relevant information.

Not sufficient
You can't dismiss Statement 2 so quickly here. If 7 of the balls are blue, then we have at most 5 red balls. If we have 5 red balls, the maximum we could have, the probability we pick 4 red balls in 4 selections is:

(5/12)(4/11)(3/10)(2/9) = 1/99

That's clearly less than 1/33, so we have enough information to be certain the answer to the question is *no* and Statement 2 is also sufficient. The answer here is D.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Wed Jun 22, 2011 12:50 am
Ian Stewart wrote:You can't dismiss Statement 2 so quickly here.
...
The answer here is D.
Thanks Ian.
Edited the reply.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Fri Dec 15, 2017 6:00 am
knight247 wrote:There are 12 balls in an urn, out of which 4 balls are picked up at random. Is the probability
of all the four balls being red greater than 1/33 ?

(1) If 2 balls are picked up, the probability of both being red is 5/33
(2) There are 7 blue balls
We are given that there are 12 balls in an urn, out of which 4 balls are picked up at random. We need to determine whether the probability of selecting 4 red balls is greater than 1/33.

Statement One Alone:

If 2 balls are picked up, the probability of both being red is 5/33

We can let r = the number of red balls and create the following equation:

(r/12) x (r - 1)/11 = 5/33

(r^2 - r)/132 = 5/33

33(r^2 - r) = 132 x 5

(r^2 - r) = 4 x 5

(r^2 - r) = 20

r^2 - r - 20 = 0

(r - 5)(r + 4) = 0

r = 5 or r = -4

Since r must be positive, we see that there are 5 red balls in the urn and thus there are 7 blue balls. Thus, we have enough information to answer the question.

Statement Two Alone:

There are 7 blue balls

Since there are 7 blue balls, there are at most 5 red balls. Even if all 5 remaining balls are red, the probability that the 4 chosen balls are red is:

(5/12) x (4/11) x (3/10) x (2/9) = 1/(11 x 9) = 1 / 99.

If there are fewer than 5 red balls in the urn, the probability that all 4 chosen balls are red is even smaller. Thus, the probability that all 4 chosen balls are red is definitely less than 1/33.

Once again, we have enough information to answer the question.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1