GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 07 Aug 2020, 00:48

### 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

# A magician has five animals in his magic hat: 3 doves and 2

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Aug 2007
Posts: 164
Schools: Life
A magician has five animals in his magic hat: 3 doves and 2  [#permalink]

### Show Tags

14 Jun 2008, 12:25
3
11
00:00

Difficulty:

25% (medium)

Question Stats:

69% (01:23) correct 31% (01:38) wrong based on 464 sessions

### HideShow timer Statistics

A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair?

A. 2/5
B. 3/5
C. 1/5
D. 1/2
E. 7/5
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10792
Location: Pune, India
Re: a magician has five animals - probability  [#permalink]

### Show Tags

06 Oct 2013, 19:56
4
2
skamran wrote:
x-ALI-x wrote:
A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair?

P(both doves) + P(both rabbits) = p(matched pair)
(3/5)*(2/4) + (2/5)*(1/4) = 2/5

Hi How did you get the probability 2/4 and 1/4???

Thanks

You have 3 doves and 2 rabbits i.e. a total of 5 animals.
The probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)
The probability that you pick a dove on your second pick too is 2/4 (because now only 2 doves are left after we picked a dove in the first pick. ALso only 4 animals are left to choose from)

Similarly,
The probability that you pick a rabbit on your first pick is 2/5 (since there are 2 rabbits)
The probability that you pick a rabbit on your second pick too is 1/4 (because now only 1 rabbit is left after we picked a rabbit in the first pick. Also only 4 animals are left to choose from)

Probability of picking a matched pair = 3/5 * 2/4 + 2/5 * 1/4 = 2/5
_________________
Karishma
Veritas Prep GMAT Instructor

Director
Joined: 14 Oct 2007
Posts: 618
Location: Oxford
Schools: Oxford'10
Re: a magician has five animals - probability  [#permalink]

### Show Tags

14 Jun 2008, 12:38
8
2
x-ALI-x wrote:
A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair?

P(both doves) + P(both rabbits) = p(matched pair)
(3/5)*(2/4) + (2/5)*(1/4) = 2/5
##### General Discussion
Intern
Joined: 06 Aug 2007
Posts: 28
Re: a magician has five animals - probability  [#permalink]

### Show Tags

14 Jun 2008, 16:44
2
3-doves, 2-rabbits

Probability that he draws 2 doves in the two turns = 3/5 * 1/3 + 2/4 * 1/2 = 9/20

Probability that he draws 2 rabbits in the two turns = 2/5 * 1/2 + 1/4 = 9/20

Total probability = 18/20

Am I totally off-course or ???
Manager
Joined: 02 Aug 2007
Posts: 164
Schools: Life
Re: a magician has five animals - probability  [#permalink]

### Show Tags

14 Jun 2008, 17:36
The OA is 40%
Good job buff, right on, better explanation than the MGMAT book.

Any other approaches are much welcome

The OE:
5c2 for 10 possible pairs, which = 10
then list the pairs in which the animals will match. Let's represent the rabbits with the letters A and B, and the doves with letters X, Y, and Z

Matched Pairs:
RaRb
DxDy
DxDz
DyDz

Therefore, the probability that the magician will randomly draw a matched set is 4/10 = 40%
Intern
Joined: 18 May 2012
Posts: 14
A magician has 5 animals in this magic hat: 3 doves and 2  [#permalink]

### Show Tags

Updated on: 08 Oct 2012, 00:29
A magician has 5 animals in this magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, which is the chance that he will have a matched pair.

P( D 1st time) and P (D 2nd time) = 3/5 x 2/4 = 3/10
or
P (R 1st time) and P (R 2nd time) 1/5 x 1/4 = 1/20

3/10 + 1/20 = 7/20

However this is wrong

Thank you!

Originally posted by chibimoon on 07 Oct 2012, 21:38.
Last edited by Bunuel on 08 Oct 2012, 00:29, edited 1 time in total.
Renamed the topic and edited the question.
VP
Joined: 02 Jul 2012
Posts: 1091
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Probability + Combinatorics: very confusing  [#permalink]

### Show Tags

07 Oct 2012, 22:40
2
chibimoon wrote:
Hi all
Q. A magician has 5 animals in this magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, which is the chance that he will have a matched pair.

P( D 1st time) and P (D 2nd time) = 3/5 x 2/4 = 3/10
or
P (R 1st time) and P (R 2nd time) 1/5 x 1/4 = 1/20

3/10 + 1/20 = 7/20

However this is wrong

Thank you!

You've worked out the probability for doves correctly. Although for the rabbits, it should be 2/5 x 1/4 = 1/10

So we would get 3/10 + 1/10 = 4/10 = 40%
Intern
Joined: 18 May 2012
Posts: 14
Re: Probability + Combinatorics: very confusing  [#permalink]

### Show Tags

07 Oct 2012, 22:42
Thank you so much, that was just a very embarrassing mistake
Intern
Joined: 04 Sep 2013
Posts: 10
Re: a magician has five animals - probability  [#permalink]

### Show Tags

06 Oct 2013, 16:24
x-ALI-x wrote:
A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair?

P(both doves) + P(both rabbits) = p(matched pair)
(3/5)*(2/4) + (2/5)*(1/4) = 2/5

Hi How did you get the probability 2/4 and 1/4???

Thanks
Senior Manager
Joined: 23 Oct 2010
Posts: 312
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Re: A magician has five animals in his magic hat: 3 doves and 2  [#permalink]

### Show Tags

04 Jan 2014, 01:25
4
1
(3C2+2C2)/5C2=2/5
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth
Manager
Joined: 20 Dec 2013
Posts: 114
Re: A magician has five animals in his magic hat: 3 doves and 2  [#permalink]

### Show Tags

04 Jan 2014, 01:44
1
1
xALIx wrote:
A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair?

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

Probability of getting a pair: Dove (Dove) + Rabbit (Rabbit) = (3/5) (2/4) + (2/5)(1/4) = (6 + 2)/20 = (8)/20 = 2/5
_________________
76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org
Intern
Joined: 01 Oct 2014
Posts: 1
GMAT Date: 11-27-2014
Re: A magician has five animals in his magic hat: 3 doves and 2  [#permalink]

### Show Tags

06 Oct 2014, 21:24
Can we interpret in the following way?

It shouldnt matter whichever animal he takes out in the first time - implies probability is 1.

What matters really is the second animal that he chooses.

As he has already chose 1 animal, so the remaining animals are 4. Hence whichever animal he pulls out will make a matched pair with the first chosen animal. Therefore the probability should be 1/4 or 25%

Whats wrong with this approach?
Intern
Joined: 12 Jul 2014
Posts: 8
Location: India
Concentration: Operations, Technology
GMAT Date: 11-06-2014
GRE 1: Q159 V144
A magician has five animals in his magic hat: 3 doves and 2  [#permalink]

### Show Tags

19 Oct 2014, 03:20
1
xALIx wrote:
A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair?

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

Hello There,
Number of total outcomes = n(S) = 5C2
Number of possible outcomes to get a matched pair = n(E) = Possible number of Combinations to get a pair from 3 Doves + Possible number of combinations to get a pair from 2 Rabbits
= 3C2 + 2C2
Probability of getting a matched pair = n(S)/n(E)
= 5C2/(3C2 + 2C2) = 2/5

_________________
Regards,
Bharat Bhushan Sunkara.

"You need to sacrifice what you are TODAY, for what you want to be TOMORROW!!"
Current Student
Joined: 10 Mar 2013
Posts: 448
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A\$)
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Re: A magician has five animals in his magic hat: 3 doves and 2  [#permalink]

### Show Tags

29 Jun 2015, 09:54
Hey there, here's an alternativ approach with combinatorics

Possible outcomes: we have repating elements here 3 Doves and 2 Rabbits --> 5!/(3!2!) = 10 outcomes
Desired outcomes: so we have two groups here, so a matched pair od Doves OR of rabitts:
Doves --> if 2 Doves are in the group 3!/(2!*1!) = 3, sam efor rabbits 2!/2!=1, so 3+1=4
Finally we have 4/10 = 2/5 (A)
Senior Manager
Joined: 28 Jun 2015
Posts: 272
Concentration: Finance
GPA: 3.5
Re: A magician has five animals in his magic hat: 3 doves and 2  [#permalink]

### Show Tags

29 Jun 2015, 10:01
3C2/5C2 + 2C2/5C2 = 3/10 + 1/10 = 4/10 = 2/5. Hence (A).
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800
Re: A magician has five animals in his magic hat: 3 doves and 2  [#permalink]

### Show Tags

12 Apr 2017, 11:02
2
1
xALIx wrote:
A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair?

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

We are given that from a group of 3 doves and 2 rabbits, 2 animals will be randomly selected. We need to determine the probability that a matched pair will be pulled out of the hat.

In other words, we need to determine:

P(2 doves pulled) + P(2 rabbits pulled)

We can use combinations to determine the number of favorable outcomes (that 2 rabbits or 2 doves are selected) and the total number of outcomes (that 2 animals are selected from 5).

Let’s first determine the number of ways we can select 2 doves from 3:

# of ways to select 2 doves from 3 doves: 3C2 = 3

Next let’s determine the number of ways we can select 2 rabbits from 2:

# of ways to select 2 rabbits from 2 rabbits: 2C2 = 1

Now we can determine the number of ways to select 2 animals from a total of 5 animals:

5C2 = (5 x 4)/(2 x 1) = 10

Thus, the probability of selecting a matched pair is 3/10 + 1/10 = 4/10 = 2/5.

_________________

# Jeffrey Miller | Head of GMAT Instruction | Jeff@TargetTestPrep.com

250 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4999
GMAT 1: 770 Q49 V46
Re: A magician has five animals in his magic hat: 3 doves and 2  [#permalink]

### Show Tags

05 Mar 2018, 14:05
Top Contributor
xALIx wrote:
A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair?

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

One approach is to apply probability rules

First notice that, to get a matched pair, we can select 2 doves or 2 rabbits.

So, P(matched pair) = P(1st pick is rabbit AND 2nd pick is rabbit OR 1st pick is dove AND 2nd pick is dove)

We can now apply our AND and OR rules to get:
P(matched pair) = [P(1st pick is rabbit) X P(2nd pick is rabbit)] + [P(1st pick is dove) X P(2nd pick is dove)]
So, P(matched pair) = [(3/5) X (2/4)] + [(2/5) X (1/4)]
= 6/20 + 2/20
= 8/20
= 2/5

RELATED VIDEO FROM OUR COURSE

_________________
If you enjoy my solutions, you'll love my GMAT prep course.

GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4999
GMAT 1: 770 Q49 V46
Re: A magician has five animals in his magic hat: 3 doves and 2  [#permalink]

### Show Tags

05 Mar 2018, 14:12
Top Contributor
xALIx wrote:
A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair?

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

We can also solve the question using counting methods

To begin, P(matched pair) = (# of ways to get a matched pair)/(# of ways to select 2 animals)

As always, begin with the denominator.
# of ways to select 2 animals
To count this, we'll treat each animal as different.
We'll take the task of selecting 2 animals and break it into stages.
Stage 1: Select the 1st animal. There are 5 animals, so this stage can be accomplished in 5 ways.
Stage 2: Select the 2nd animal. There are now 4 animals remaining, so this stage can be accomplished in 4 ways.
So, the total number of ways to select 2 animals is (5)(4), which equals 20

Now the numerator.

# of ways to get a matched pair
We need to consider two cases.

Case 1: select 2 doves.
In how many different ways can this occur?
Well, we'll take the task of selecting 2 doves and break it into stages.
Stage 1: Select the 1st dove. There are 3 doves, so this stage can be accomplished in 3 ways.
Stage 2: Select the 2nd dove. There are now 2 doves remaining, so this stage can be accomplished in 2 ways.
So, the total number of ways to select 2 doves is (3)(2), which equals 6

Case 2: select 2 rabbits.
In how many different ways can this occur?
Well, we'll take the task of selecting 2 rabbits and break it into stages.
Stage 1: Select the 1st rabbit. There are 2 rabbits, so this stage can be accomplished in 2 ways.
Stage 2: Select the 2nd rabbit. There is now 1 rabbit remaining, so this stage can be accomplished in 1 ways.
So, the TOTAL number of ways to select 2 rabbits is (2)(1), which equals 2

Put it all together to get:
P(matched pair) = (6+2)/(20)
= 8/20
= 2/5
= A

Cheers,
Brent
_________________
If you enjoy my solutions, you'll love my GMAT prep course.

Intern
Joined: 12 Sep 2017
Posts: 26
Re: A magician has five animals in his magic hat: 3 doves and 2  [#permalink]

### Show Tags

10 Apr 2018, 03:19
TimeTraveller wrote:
3C2/5C2 + 2C2/5C2 = 3/10 + 1/10 = 4/10 = 2/5. Hence (A).

Hi

I am little confused in which case we select two things one by one and in which case both together. why are we not selecting 3c1*2C1 + 2C1*1C1 ?
Non-Human User
Joined: 09 Sep 2013
Posts: 15625
Re: A magician has five animals in his magic hat: 3 doves and 2  [#permalink]

### Show Tags

22 Nov 2019, 08:14
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.
_________________
Re: A magician has five animals in his magic hat: 3 doves and 2   [#permalink] 22 Nov 2019, 08:14