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

 It is currently 06 May 2015, 06:13

### 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

# There are 18 shirts in a closet. 12 are stripes and 6 are

Author Message
TAGS:
Current Student
Joined: 31 Aug 2007
Posts: 371
Followers: 1

Kudos [?]: 54 [0], given: 1

There are 18 shirts in a closet. 12 are stripes and 6 are [#permalink]  31 Mar 2008, 15:55
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
There are 18 shirts in a closet. 12 are stripes and 6 are white. 6 draws are made of 1 shirt at a time without any replacement of which at least 4 are found to be white. What is the probability that in the next 2 draws, exactly 1 shirt is white?
Director
Joined: 10 Sep 2007
Posts: 949
Followers: 7

Kudos [?]: 206 [0], given: 0

Re: PS probability--shirts [#permalink]  31 Mar 2008, 16:11
After 4 whites are gone, the there are only 2 white shirts left in the closet.
So number of ways 1 shirt can be chosen from 2 shirts = 2C1 = 2

There are total of 12 stripes.
So number of ways 1 stripes shirt can be chosen from 12 shirts = 12C1 = 12

Total number of shirts in closet = 2 + 12 = 14
Total number of ways of selecting 2 shirts from 14 = 14C2 = 91

So probability = 2*12/91 = 24/91

However please note that white shirt can be chosen first and stripes second and vice-versa is also possible.
So final probability needs to be multiplied by 2!.

Probability = 24*2!/19 = 48/91
Senior Manager
Joined: 01 Feb 2005
Posts: 274
Followers: 1

Kudos [?]: 39 [0], given: 1

Re: PS probability--shirts [#permalink]  31 Mar 2008, 16:39
Can you explain this part of your answer? I did not understand this. I got till 14C2 = 91

So probability = 2*12/91 = 24/91

However please note that white shirt can be chosen first and stripes second and vice-versa is also possible.
So final probability needs to be multiplied by 2!.

Probability = 24*2!/19 = 48/91
Director
Joined: 10 Sep 2007
Posts: 949
Followers: 7

Kudos [?]: 206 [0], given: 0

Re: PS probability--shirts [#permalink]  31 Mar 2008, 16:48
Question tells us that out of remaining 2 shirts 1 has to be white and other 1 has to be stripes. But question does not tells you the order in which they will be drawn.
So for 1 case, white can be first drawn and stripes can be drawn later.
But it is also possible that stripes is drawn first and then white is drawn later.
Thereby there are 2 ways by which we can draw one white and one stripes from the closet.
Senior Manager
Joined: 20 Feb 2008
Posts: 296
Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross
Followers: 4

Kudos [?]: 38 [0], given: 0

Re: PS probability--shirts [#permalink]  31 Mar 2008, 16:51
Thank you
Current Student
Joined: 31 Aug 2007
Posts: 371
Followers: 1

Kudos [?]: 54 [0], given: 1

Re: PS probability--shirts [#permalink]  01 Apr 2008, 08:38
sorry, i don't have the OA for this one.
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 407

Kudos [?]: 2149 [0], given: 359

Re: PS probability--shirts [#permalink]  01 Apr 2008, 10:58
Expert's post
young_gun wrote:
There are 18 shirts in a closet. 12 are stripes and 6 are white. 6 draws are made of 1 shirt at a time without any replacement of which at least 4 are found to be white. What is the probability that in the next 2 draws, exactly 1 shirt is white?

First of all, I would say that this problem is not like GMAT one.

Here, we have two events:

1. 6 draws are made of 1 shirt at a time without any replacement of which at least 4 are found to be white.
So, we have to consider 3 possibilities: 4 white and 2 stripes shirts, 5 white and 1 stripes shirts, and 6 white and 0 stripes shirts:

a) 4 white and 2 stripes shirts: the number of combination: $$N_a=C^6_4*C^{12}_2=\frac{6*5}{2}*\frac{12*11}{2}=990$$

b) 5 white and 1 stripes shirts: the number of combination: $$N_b=C^6_5*C^{12}_1=6*12=72$$

c) 6 white and 0 stripes shirts: the number of combination: $$N_c=C^6_6*C^{12}_0=1*1=1$$

Therefore, the probabilities will be:

a) $$p_a=\frac{990}{990+72+1}=\frac{990}{1063}$$

b) $$p_b=\frac{72}{1063}$$

c) $$p_c=\frac{1}{1063}$$

2. in the next 2 draws, exactly 1 shirt is white

a) $$q_{a}=\frac{990}{1063}*\frac{C^2_1*C^{10}_1}{C^{14}_2}=\frac{990}{1063}*\frac{40}{182}$$

b) $$q_{b}=\frac{72}{1063}*\frac{C^1_1*C^{11}_1}{C^{14}_2}=\frac{72}{1063}*\frac{22}{182}$$

c) $$q_{c}=\frac{72}{1063}*0=0$$

Finally,

$$P=q_a+q_b+q_c =\frac{990}{1063}*\frac{40}{182}+\frac{72}{1063}*\frac{22}{182}+0 =\frac{1062}{1063}*\frac{62}{182} = \frac{1062}{1063}*\frac{31}{91}$$

I understand that I am wrong but do not understand where I am wrong
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Director
Joined: 10 Sep 2007
Posts: 949
Followers: 7

Kudos [?]: 206 [0], given: 0

Re: PS probability--shirts [#permalink]  01 Apr 2008, 16:38
walker wrote:
young_gun wrote:
There are 18 shirts in a closet. 12 are stripes and 6 are white. 6 draws are made of 1 shirt at a time without any replacement of which at least 4 are found to be white. What is the probability that in the next 2 draws, exactly 1 shirt is white?

I understand that I am wrong but do not understand where I am wrong

First of all question is saying 4 shirts are already drawn they are all white. So that part is already out of scope, no need to factor that calculating final probability. Moreover question is saying that in remaining 2 shirts exactly 1 of them should be white, so cases of 6 white and 4 white and 2 stripes become invalid and should not be factored for final calculations.
Director
Joined: 14 Aug 2007
Posts: 734
Followers: 8

Kudos [?]: 118 [0], given: 0

Re: PS probability--shirts [#permalink]  01 Apr 2008, 22:30
young_gun wrote:
There are 18 shirts in a closet. 12 are stripes and 6 are white. 6 draws are made of 1 shirt at a time without any replacement of which at least 4 are found to be white. What is the probability that in the next 2 draws, exactly 1 shirt is white?

My take

2 things to note:
A. without any replacement
B.at least 4 are found to be white

A =>
6 shirts are already out so total number of shirts is 12 for next 2 draws.

B =>
we have 3 cases
Case 1)4 white shirts and 2 striped shirts taken out => 2 white & 10 striped remain
Case 2)5 white shirts and 1 striped shirt taken out => 1 white and 11 striped remain
Case 3)6 white shirts and 0 striped shirt takes out => 0 white and 12 striped remain

What we want is
>the probability that in the next 2 draws, exactly 1 shirt is white?

for case 1
P(W|S) = ( 2/12 * 10/11) / 10/11 OR
P(S|W) = (10/12 * 2/11)/ 2/11

P(case 1) = 1 (????)

for case 2

P(W|S) = ( 1/12 * 11/11) / 11/11 OR
P(S|W) = (11/12 * 1/11)/ 1/11

so case 3) is ignored as no white shirts present. = 0

&.... I have screwed somewhere!
Re: PS probability--shirts   [#permalink] 01 Apr 2008, 22:30
Similar topics Replies Last post
Similar
Topics:
2 If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from 2 01 Mar 2015, 00:07
1 M18-12 3 16 Sep 2014, 00:03
1 M12-18 4 15 Sep 2014, 23:47
There are 18 shirts in a closet. 12 are stripes and 6 are 14 18 May 2006, 17:33
6 In a drawer of shirts 8 are blue, 6 are green and 4 are 14 11 Dec 2005, 19:07
Display posts from previous: Sort by