GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 02:02 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 wh

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Senior Manager  D
Joined: 18 Jun 2018
Posts: 262
Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 wh  [#permalink]

Show Tags

1
9 00:00

Difficulty:   95% (hard)

Question Stats: 13% (02:05) correct 87% (02:15) wrong based on 39 sessions

HideShow timer Statistics

Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 white balls and 2 black balls. One ball is picked from urn 1 and dropped in urn 2. Then one ball is picked from urn 2. If this ball turns out to be white, find the probability that the ball taken from urn 1 and dropped in urn 2 is also white.

(A) $$\frac{5}{12}$$

(B) $$\frac{7}{12}$$

(C) $$\frac{1}{2}$$

(D) $$\frac{5}{13}$$

(E) $$\frac{6}{13}$$

Originally posted by Bismarck on 06 Oct 2018, 03:06.
Last edited by Bismarck on 14 Oct 2018, 05:29, edited 1 time in total.
Intern  B
Joined: 10 Jul 2018
Posts: 7
Location: India
Schools: ESMT
GMAT 1: 700 Q44 V44 GPA: 3.54
Re: Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 wh  [#permalink]

Show Tags

1
I am not sure if the picking white ball will have an impact on the probability to pick white ball from Urn 1.

My take is:
* We can select white ball from Urn 1 in 5C1 ways
* Total #ways to pick a ball from Urn 1 is 13C1
* Hence, the probability to pick white ball from Urn 1 = 5C1/13C1 = 5/13.

Option D
Director  D
Joined: 28 Jul 2016
Posts: 613
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 wh  [#permalink]

Show Tags

Bismarck wrote:
Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 white balls and 2 black balls. One ball is picked from urn 1 and dropped in urn 2. Then one ball is picked from urn 2. If this ball turns out to be white, find the probability that the ball taken from urn 1 and dropped in urn 2 is also white.

(A) $$\frac{5}{12}$$

(B) $$\frac{7}{12}$$

(C) $$\frac{1}{2}$$

(D) $$\frac{5}{13}$$

(E) $$\frac{6}{13}$$

Bismarck.. Is the answer to the question correct.
It does not matter what the probability of ball picked up from Urn 2 is.
chetan2u can you help with this question
Intern  B
Joined: 27 Aug 2018
Posts: 1
Re: Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 wh  [#permalink]

Show Tags

So the probability that the Ball picked from urn 2 is white, could be
1. either 7/10, if the ball dropped from urn 1 is Black.
2 or, 8/10, if the ball picked from urn 1 is white.

If the ball picked and dropped from urn 1 to urn 2 is white, (as per the ques); then the probability of the ball picked from urn 2 = 8/10 = 4/5

Hence the probability that a ball picked from urn 1 is white AND the ball picked from urn 2 is white = 5/8 * 4/5 = 1/2

Director  D
Joined: 28 Jul 2016
Posts: 613
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 wh  [#permalink]

Show Tags

PALL07 wrote:
So the probability that the Ball picked from urn 2 is white, could be
1. either 7/10, if the ball dropped from urn 1 is Black.
2 or, 8/10, if the ball picked from urn 1 is white.

If the ball picked and dropped from urn 1 to urn 2 is white, (as per the ques); then the probability of the ball picked from urn 2 = 8/10 = 4/5

Hence the probability that a ball picked from urn 1 is white AND the ball picked from urn 2 is white = 5/8 * 4/5 = 1/2

PALL07 I agree with your solution, however, that is the probability of the entire outcome.
Question jut asks for the probability of first urn.
Senior Manager  D
Joined: 18 Jun 2018
Posts: 262
Re: Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 wh  [#permalink]

Show Tags

2
1
OA: A

Following combinations are possible : WW,WB,BW,BB
Probability of each case
WW ( 1st Urn : White ;2nd Urn : White) $$: \frac{5}{13}*\frac{8}{10}=\frac{40}{130}$$
WB ( 1st Urn : White ; 2nd Urn : Black) $$: \frac{5}{13}*\frac{2}{10}=\frac{10}{130}$$
BW ( 1st Urn : Black ; 2nd Urn : White) $$: \frac{8}{13}*\frac{7}{10}=\frac{56}{130}$$
BB ( 1st Urn : Black ; 2nd Urn : Black) $$: \frac{8}{13}*\frac{3}{10}=\frac{24}{130}$$

Probability of 1 st ball being white , given 2nd ball is white$$= \frac{WW}{WW+BW} =\frac{\frac{40}{130}}{\frac{40}{130}+\frac{56}{130}}=\frac{40}{96}=\frac{5}{12}$$
Director  P
Joined: 24 Nov 2016
Posts: 624
Location: United States
Re: Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 wh  [#permalink]

Show Tags

Bismarck wrote:
OA: A

Following combinations are possible : WW,WB,BW,BB
Probability of each case
WW ( 1st Urn : White ;2nd Urn : White) $$: \frac{5}{13}*\frac{8}{10}=\frac{40}{130}$$
WB ( 1st Urn : White ; 2nd Urn : Black) $$: \frac{5}{13}*\frac{2}{10}=\frac{10}{130}$$
BW ( 1st Urn : Black ; 2nd Urn : White) $$: \frac{8}{13}*\frac{7}{10}=\frac{56}{130}$$
BB ( 1st Urn : Black ; 2nd Urn : Black) $$: \frac{8}{13}*\frac{3}{10}=\frac{24}{130}$$

Probability of 1 st ball being white , given 2nd ball is white$$= \frac{WW}{WW+BW} =\frac{\frac{40}{130}}{\frac{40}{130}+\frac{56}{130}}=\frac{40}{96}=\frac{5}{12}$$

Why did you divide WW?
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 wh  [#permalink]

Show Tags

1
1
Bismarck wrote:
Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 white balls and 2 black balls. One ball is picked from urn 1 and dropped in urn 2. Then one ball is picked from urn 2. If this ball turns out to be white, find the probability that the ball taken from urn 1 and dropped in urn 2 is also white.

(A) $$\frac{5}{12}$$

(B) $$\frac{7}{12}$$

(C) $$\frac{1}{2}$$

(D) $$\frac{5}{13}$$

(E) $$\frac{6}{13}$$

This is a question on conditional probability.

P (X given Y) = P("first ball is white" given "second ball is white")

P(first ball is white and second is white ) = (5/13) * (8/10) = 40/130
P (second ball is white) = (5/13)*(8/10) + (8/13)*(7/10) = (40 + 56)/130 = 96/130

P(X given Y) = P(first ball is white and second is white )/P (second ball is white) = (40/130) / (96/130) = 5/12

Check this post on conditional probability: https://www.veritasprep.com/blog/2012/0 ... onditions/
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Re: Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 wh   [#permalink] 04 Oct 2019, 05:17
Display posts from previous: Sort by

Urn 1 contains 5 white balls and 8 black balls and Urn 2 contains 7 wh

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  