It is currently 22 Oct 2017, 23:28

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A jar contains 4 black and 3 white balls. If you pick two ba

Author Message
TAGS:

### Hide Tags

BSchool Forum Moderator
Joined: 27 Aug 2012
Posts: 1188

Kudos [?]: 1928 [0], given: 152

A jar contains 4 black and 3 white balls. If you pick two ba [#permalink]

### Show Tags

30 Aug 2013, 06:09
2
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

65% (00:52) correct 35% (01:22) wrong based on 190 sessions

### HideShow timer Statistics

A jar contains 4 black and 3 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?

A. 2/7
B. 5/7
C. 4/7
D. 3/7
E. 1/2
[Reveal] Spoiler: OA

_________________

Last edited by bagdbmba on 30 Aug 2013, 06:45, edited 1 time in total.

Kudos [?]: 1928 [0], given: 152

Math Expert
Joined: 02 Sep 2009
Posts: 41908

Kudos [?]: 129394 [1], given: 12197

Re: A jar contains 4 black and 3 white balls.If you pick two [#permalink]

### Show Tags

30 Aug 2013, 06:27
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
bagdbmba wrote:
A jar contains 4 black and 3 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?

A. 2/7
B. 5/7
C. 4/7
D. 3/7
E. 1/2

P(1st black, 2nd white) = 4/7*3/6 = 4/14;
P(1st white, 2nd black) = 3/7*4/6 = 4/14.

P = 4/14 + 4/14 = 4/7.

OR: $$P=\frac{C^1_4*C^1_3}{C^2_7}=\frac{4}{7}$$

OA is NOT correct.
_________________

Kudos [?]: 129394 [1], given: 12197

BSchool Forum Moderator
Joined: 27 Aug 2012
Posts: 1188

Kudos [?]: 1928 [0], given: 152

Re: A jar contains 4 black and 3 white balls. If you pick two ba [#permalink]

### Show Tags

30 Aug 2013, 06:48
Thanks Bunuel for pointing it out...Corrected the OA accordingly in the question...
_________________

Kudos [?]: 1928 [0], given: 152

BSchool Forum Moderator
Joined: 27 Aug 2012
Posts: 1188

Kudos [?]: 1928 [0], given: 152

Re: A jar contains 4 black and 3 white balls.If you pick two [#permalink]

### Show Tags

05 Sep 2013, 09:26
Bunuel wrote:
bagdbmba wrote:
A jar contains 4 black and 3 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?

A. 2/7
B. 5/7
C. 4/7
D. 3/7
E. 1/2

P(1st black, 2nd white) = 4/7*3/6 = 4/14;
P(1st white, 2nd black) = 3/7*4/6 = 4/14.

P = 4/14 + 4/14 = 4/7.

OR: $$P=\frac{C^1_4*C^1_3}{C^2_7}=\frac{4}{7}$$

OA is NOT correct.

Hi Bunuel,
As per the above explanation - why the OA of the following problem is NOT 3/10?
http://gmatclub.com/forum/x-y-and-z-are-all-unique-numbers-if-x-is-chosen-randomly-159208.html

_________________

Kudos [?]: 1928 [0], given: 152

Manager
Joined: 23 May 2013
Posts: 122

Kudos [?]: 67 [0], given: 110

Re: A jar contains 4 black and 3 white balls.If you pick two [#permalink]

### Show Tags

08 Sep 2013, 04:07
Bunuel wrote:
bagdbmba wrote:
A jar contains 4 black and 3 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?

A. 2/7
B. 5/7
C. 4/7
D. 3/7
E. 1/2

P(1st black, 2nd white) = 4/7*3/6 = 4/14;
P(1st white, 2nd black) = 3/7*4/6 = 4/14.

P = 4/14 + 4/14 = 4/7.

OR: $$P=\frac{C^1_4*C^1_3}{C^2_7}=\frac{4}{7}$$

OA is NOT correct.

Hi Bunuel

I wanted to know if probability approach can be used to resolve any sort of probability problem. I am quite comfortable with it. when is it advantageous to use combination approach?
_________________

“Confidence comes not from always being right but from not fearing to be wrong.”

Kudos [?]: 67 [0], given: 110

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16542

Kudos [?]: 274 [0], given: 0

Re: A jar contains 4 black and 3 white balls. If you pick two ba [#permalink]

### Show Tags

16 Mar 2015, 12:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 274 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16542

Kudos [?]: 274 [0], given: 0

Re: A jar contains 4 black and 3 white balls. If you pick two ba [#permalink]

### Show Tags

06 Jul 2016, 11:39
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 274 [0], given: 0

Director
Joined: 19 Mar 2014
Posts: 941

Kudos [?]: 220 [0], given: 188

Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: A jar contains 4 black and 3 white balls. If you pick two ba [#permalink]

### Show Tags

28 Jun 2017, 13:22
Bunuel wrote:
bagdbmba wrote:
A jar contains 4 black and 3 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?

A. 2/7
B. 5/7
C. 4/7
D. 3/7
E. 1/2

P(1st black, 2nd white) = 4/7*3/6 = 4/14;
P(1st white, 2nd black) = 3/7*4/6 = 4/14.

P = 4/14 + 4/14 = 4/7.

OR: $$P=\frac{C^1_4*C^1_3}{C^2_7}=\frac{4}{7}$$

OA is NOT correct.

Hello Bunuel and VeritasPrepKarishma

As per Veritas the answer is 2/7

And the logical argument is that event is happening simultaneously hence we will only consider one scenario of removing the balls.

Could you please confirm what should be the correct strategy and what is the correct answer?

We are now confused between 4/7 & 2/7
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Worried About IDIOMS? Here is a Daily Practice List: https://gmatclub.com/forum/idiom-s-ydmuley-s-daily-practice-list-250731.html#p1937393

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Kudos [?]: 220 [0], given: 188

Math Expert
Joined: 02 Sep 2009
Posts: 41908

Kudos [?]: 129394 [0], given: 12197

Re: A jar contains 4 black and 3 white balls. If you pick two ba [#permalink]

### Show Tags

28 Jun 2017, 13:33
ydmuley wrote:
Bunuel wrote:
bagdbmba wrote:
A jar contains 4 black and 3 white balls. If you pick two balls at the same time, what's the probability that one ball is black and one is white?

A. 2/7
B. 5/7
C. 4/7
D. 3/7
E. 1/2

P(1st black, 2nd white) = 4/7*3/6 = 4/14;
P(1st white, 2nd black) = 3/7*4/6 = 4/14.

P = 4/14 + 4/14 = 4/7.

OR: $$P=\frac{C^1_4*C^1_3}{C^2_7}=\frac{4}{7}$$

OA is NOT correct.

Hello Bunuel and VeritasPrepKarishma

As per Veritas the answer is 2/7

And the logical argument is that event is happening simultaneously hence we will only consider one scenario of removing the balls.

Could you please confirm what should be the correct strategy and what is the correct answer?

We are now confused between 4/7 & 2/7

Mathematically the probability of picking two balls simultaneously, or picking them one at a time (without replacement) is the same. The correct answer is 4/7.
_________________

Kudos [?]: 129394 [0], given: 12197

Director
Joined: 19 Mar 2014
Posts: 941

Kudos [?]: 220 [0], given: 188

Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: A jar contains 4 black and 3 white balls. If you pick two ba [#permalink]

### Show Tags

28 Jun 2017, 13:40
Hello Bunuel and VeritasPrepKarishma

As per Veritas the answer is 2/7

And the logical argument is that event is happening simultaneously hence we will only consider one scenario of removing the balls.

Could you please confirm what should be the correct strategy and what is the correct answer?

We are now confused between 4/7 & 2/7[/quote]
Bunuel wrote:

Mathematically the probability of picking two balls simultaneously, or picking them one at a time (without replacement) is the same. The correct answer is 4/7.

Ok.. thanks Bunuel - will go with 4/7

VeritasPrepKarishma - Not sure if you agree to this, in case the books have to be changed to avoid confusion going forward.
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Worried About IDIOMS? Here is a Daily Practice List: https://gmatclub.com/forum/idiom-s-ydmuley-s-daily-practice-list-250731.html#p1937393

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Kudos [?]: 220 [0], given: 188

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7677

Kudos [?]: 17398 [0], given: 232

Location: Pune, India
A jar contains 4 black and 3 white balls. If you pick two ba [#permalink]

### Show Tags

29 Jun 2017, 04:56
ydmuley wrote:
Hello Bunuel and VeritasPrepKarishma

As per Veritas the answer is 2/7

And the logical argument is that event is happening simultaneously hence we will only consider one scenario of removing the balls.

Could you please confirm what should be the correct strategy and what is the correct answer?

We are now confused between 4/7 & 2/7

Bunuel wrote:

Mathematically the probability of picking two balls simultaneously, or picking them one at a time (without replacement) is the same. The correct answer is 4/7.

Ok.. thanks Bunuel - will go with 4/7

VeritasPrepKarishma - Not sure if you agree to this, in case the books have to be changed to avoid confusion going forward.

Responding to a pm:

The answer is certainly 4/7 and that is what the book says too.
The book shows that "2 simultaneous picks" is the same as "pick one and then another". So getting one black and one white can be achieved in 2 ways: a black and then a white or a white and then a black. I agree that the addition isn't explicitly shown but "pick two such that one is black and one is white" is composed of two cases:
First black and then white for which Probability = 2/7
First white and then black for which Probability = 2/7
They both result in one white and one black so answer would be 4/7.

Note that there are only 2 other cases:
Both black for which probability = 4/7 * 3/6 = 2/7
Both white for which probability = 3/7 * 2/6 = 1/7

Overall probability = 2/7 + 2/7 + 2/7 + 1/7 = 1
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17398 [0], given: 232

A jar contains 4 black and 3 white balls. If you pick two ba   [#permalink] 29 Jun 2017, 04:56
Display posts from previous: Sort by