Find all School-related info fast with the new School-Specific MBA Forum

It is currently 16 Sep 2014, 19:39

Close

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
Your Progress

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Magician with the rabits

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29655
Followers: 3492

Kudos [?]: 26236 [1] , given: 2707

Magician with the rabits [#permalink] New post 10 Oct 2009, 18:21
1
This post received
KUDOS
Expert's post
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

38% (02:46) correct 63% (00:28) wrong based on 18 sessions
Try this one:

Magician has a rabbit in the hat, it's either white or black (probability 50/50). He adds one more rabbit in the hat which is white and then he randomly picks one which turns out to be white. What is the probability that the remaining rabbit in the hat is also white?

A. 0
B. 1/3
C. 1/2
D. 2/3
E. 1.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

CEO
CEO
User avatar
Joined: 29 Aug 2007
Posts: 2501
Followers: 53

Kudos [?]: 505 [0], given: 19

GMAT Tests User
Re: Magician with the rabits [#permalink] New post 10 Oct 2009, 20:24
Bunuel wrote:
Magician has a rabbit in the hat, it's either white or black (probability 50/50). He adds one more rabbit in the hat which is white and then he randomly picks one which turns out to be white. What is the probability that the remaining rabbit in the hat is also white?

A. 0
B. 1/3
C. 1/2
D. 2/3
E. 1.


The second one could be either white or black.

P (white) = white (p) + (1- black)(p)
P (white) = 1 (1/2) + 0 (1/2)
P (white) = 1/2
_________________

Verbal: new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

Intern
Intern
avatar
Joined: 02 Oct 2009
Posts: 16
Followers: 0

Kudos [?]: 7 [0], given: 5

Re: Magician with the rabits [#permalink] New post 10 Oct 2009, 22:03
I think 1/2 should be the ans :oops:

Last edited by rvthryet on 10 Oct 2009, 23:50, edited 1 time in total.
Manager
Manager
avatar
Joined: 11 Sep 2009
Posts: 129
Followers: 4

Kudos [?]: 172 [0], given: 6

GMAT Tests User
Re: Magician with the rabits [#permalink] New post 10 Oct 2009, 22:16
Good question. A bit tricky to get your head around it because you have to approach it using conditional probabilities in reverse to some extent. I believe the answer is 2/3.

To Start:

Rabbit 1: 50/50 White/Black
Rabbit 2: 100 White

Now we know that the first rabbit picked was white. Therefore, there's a 2/3 chance that Rabbit 2 was picked, and 1/3 chance Rabbit 1 was picked, based on conditional probability (we know a black rabbit WAS NOT picked, so we can say 2 out of 3 times, Rabbit 2 was picked).

Therefore,

If rabbit 1 was picked initially (P = 1/3): 100% chance a white rabbit will be picked next.
If rabbit 2 was picked initially (P = 2/3): 50% chance a white rabbit will be picked next.

P(white rabbit will be picked) = (1/3)(1) + (2/3)(1/2) = 2/3

If anyone needs clarification on that, I'll try and explain in more detail. Good question, +1.
Manager
Manager
User avatar
Joined: 01 Jan 2009
Posts: 96
Location: India
Schools: LBS
Followers: 2

Kudos [?]: 44 [0], given: 6

Re: Magician with the rabits [#permalink] New post 10 Oct 2009, 22:22
I have a small doubt...

can we change the problem slightly to make it more simple, without changing the meaning though.

i.e. we say that the hat already had 1 black and 1 white rabbit.

so P(Black initial) = 1/2 and P(White initial) = 1/2 remain the same.

This way it becomes simpler. But has the meaning changed? :roll:
_________________

The Legion dies, it does not surrender.

Intern
Intern
avatar
Joined: 02 Oct 2009
Posts: 16
Followers: 0

Kudos [?]: 7 [0], given: 5

Re: Magician with the rabits [#permalink] New post 10 Oct 2009, 23:39
Let me put this question in a different way.. Imagine you have two coins

1st is a fair coin with a Head and a Tail.
2nd is a coin with only a head ( so u'll only get a head in each flip)

You have four possible outcomes in this case H, T, H, H. Out of this favourable outcomes are 3(H,H,H). So,

P(getting head in the 1st trial) = 3/4.

After the first trial only one coin is left. Since we do not know out of the two which coin is removed the possible outcomes are H,T and favourable is only 1. So,

P(getting a head in second trial)= 1/2.

Therefore, the ans to the question should be 1/2

This just seems very logical.. though i do not know if it is correct :? Probability has never been my forte.. Pls let me know where am i wrong
Director
Director
avatar
Joined: 12 Jun 2006
Posts: 539
Followers: 1

Kudos [?]: 14 [0], given: 1

GMAT Tests User
Re: Magician with the rabits [#permalink] New post 11 Oct 2009, 12:25
Do we have an OA for this?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29655
Followers: 3492

Kudos [?]: 26236 [0], given: 2707

Re: Magician with the rabits [#permalink] New post 11 Oct 2009, 12:40
Expert's post
Director
Director
avatar
Joined: 12 Jun 2006
Posts: 539
Followers: 1

Kudos [?]: 14 [0], given: 1

GMAT Tests User
Re: Magician with the rabits [#permalink] New post 11 Oct 2009, 16:33
I did. I'm getting 1/2---which, at this point, I'm sure is wrong.
Senior Manager
Senior Manager
avatar
Joined: 18 Aug 2009
Posts: 333
Followers: 8

Kudos [?]: 166 [0], given: 13

GMAT Tests User
Re: Magician with the rabits [#permalink] New post 11 Oct 2009, 18:36
Here is what I think:

The probability that the first rabit is white = 1/2.
So after adding the second rabit, we have combination: {W, W, B}
First rabit is W, so remaining combination is: {W, B}
So again the probability that the rabit is White = 1/2.
:roll:
Director
Director
avatar
Joined: 12 Jun 2006
Posts: 539
Followers: 1

Kudos [?]: 14 [0], given: 1

GMAT Tests User
Re: Magician with the rabits [#permalink] New post 11 Oct 2009, 19:20
I thought about this again and Prodigy's expl. makes sense to me. Things can shake out one of two ways:

Instance 1
w/b (scenario 1)
w/w (scenario 2)

or

Instance 2
w/b (scenario 1)
w/w (scenario 2)

Let's assume that the bolded Ws are the white rabbits "randomly pick[ed]" in each instance. Once the bolded W is chosen, there are 2 out of 3 chances of another W being chosen. I hope that this makes sense---and more importantly, is correct.
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29655
Followers: 3492

Kudos [?]: 26236 [2] , given: 2707

Re: Magician with the rabits [#permalink] New post 12 Oct 2009, 15:30
2
This post received
KUDOS
Expert's post
SOLUTION:

This is longknow probability problem.

After picking white rabbit there are three equally likely states:

In the hat could be:

1. White rabbit, which was there initially (picked the white we put);
2. Black rabbit, which was there initially (picked the white we put);
3. White rabbit, which we put (picked the white was there initially)

Thus probability of picking the white is 2/3.

P.S. Posted the solutions to the tough & tricky problems set at: tough-tricky-set-of-problms-85211.html#p638370
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 18 Aug 2009
Posts: 437
Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0
Followers: 6

Kudos [?]: 48 [0], given: 16

GMAT Tests User
Re: Magician with the rabits [#permalink] New post 12 Oct 2009, 20:40
But, I can not follow the logic.
If problem sounds like this :

The magician has two rabbits in the hat: black and white (so their probability of being chosen is 1/2)
Then one more white rabbit is put over there, thus the probability of choosing a rabbit increased to 2/3 (probability of choosing black is 1/3)
Then white rabbit is removed. Thus only one black rabbit and one white rabbit is left, thus it means the probability should be
1/2

Is n't the problem the same, with the one you put?
_________________

Never give up,,,

Manager
Manager
avatar
Joined: 11 Sep 2009
Posts: 129
Followers: 4

Kudos [?]: 172 [0], given: 6

GMAT Tests User
Re: Magician with the rabits [#permalink] New post 12 Oct 2009, 21:50
mirzohidjon wrote:
But, I can not follow the logic.
If problem sounds like this :

The magician has two rabbits in the hat: black and white (so their probability of being chosen is 1/2)
Then one more white rabbit is put over there, thus the probability of choosing a rabbit increased to 2/3 (probability of choosing black is 1/3)
Then white rabbit is removed. Thus only one black rabbit and one white rabbit is left, thus it means the probability should be
1/2

Is n't the problem the same, with the one you put?


You would need to put two more white rabbits to compensate for the fact that you are treating the original rabbit as two rabbits.
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1365
Followers: 11

Kudos [?]: 140 [0], given: 10

GMAT Tests User
Re: Magician with the rabits [#permalink] New post 03 May 2011, 22:43
interesting solution.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Manager
Manager
avatar
Joined: 14 Mar 2011
Posts: 92
Followers: 1

Kudos [?]: 3 [0], given: 3

Re: Magician with the rabits [#permalink] New post 04 May 2011, 01:13
Bunuel wrote:
SOLUTION:

This is longknow probability problem.

After picking white rabbit there are three equally likely states:

In the hat could be:

1. White rabbit, which was there initially (picked the white we put);
2. Black rabbit, which was there initially (picked the white we put);
3. White rabbit, which we put (picked the white was there initially)

Thus probability of picking the white is 2/3.

P.S. Posted the solutions to the tough & tricky problems set at: tough-tricky-set-of-problms-85211.html#p638370


I think that there is a problem with this solution because the 3 cases mentions above do not have the same probability of being true. It is not like the case we have 3 balls in a basket (2 white and 1 black). In this case the probability of picking a white ball is 2/3.

Do you have any official source of this problem?

Thank you.
Re: Magician with the rabits   [#permalink] 04 May 2011, 01:13
    Similar topics Author Replies Last post
Similar
Topics:
Turn-of- the century magician Harry claimed, for his famous Archit143 0 04 Apr 2013, 23:47
14 A magician has five animals in his magic hat: 3 doves and 2 xALIx 11 14 Jun 2008, 12:25
2 Experts publish their posts in the topic A magician holds one six-sided die in his left hand and two carcass 9 15 May 2012, 16:52
1 Turn-of-the-century magician Harry Houdini claimed, for his yvonne0923 9 09 May 2011, 19:29
Ok I got one for ya, you MatheMagicians When positive vikramjit_01 6 11 Apr 2007, 13:14
Display posts from previous: Sort by

Magician with the rabits

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.