It is currently 23 Jan 2018, 22:05

### 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

# D01-37

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43380

### Show Tags

15 Sep 2014, 23:13
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:16) correct 20% (01:15) wrong based on 117 sessions

### HideShow timer Statistics

A box contains 11 hats, out of which 6 are red hats and 5 are green hats. If two hats are to be selected at random without replacement, what is the probability that at least one green hat will be selected?

A. $$\frac{10}{11}$$
B. $$\frac{8}{11}$$
C. $$\frac{7}{12}$$
D. $$\frac{5}{13}$$
E. $$\frac{2}{7}$$
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 43380

### Show Tags

15 Sep 2014, 23:13
Expert's post
1
This post was
BOOKMARKED
Official Solution:

A box contains 11 hats, out of which 6 are red hats and 5 are green hats. If two hats are to be selected at random without replacement, what is the probability that at least one green hat will be selected?

A. $$\frac{10}{11}$$
B. $$\frac{8}{11}$$
C. $$\frac{7}{12}$$
D. $$\frac{5}{13}$$
E. $$\frac{2}{7}$$

It's easier to find the probability of the opposite event and subtract it from 1. The opposite event would be if we select zero green hats, or which is the same if we select 2 red hats, so: $$P(G \ge 1)=1-P(RR)=1-\frac{6}{11}*\frac{5}{10}=\frac{8}{11}$$.

_________________
Current Student
Joined: 03 Oct 2014
Posts: 139
Location: India
Concentration: Operations, Technology
GMAT 1: 720 Q48 V40
WE: Engineering (Aerospace and Defense)

### Show Tags

12 Jan 2015, 21:43
Option B - (1-6C2/11C2)
Current Student
Joined: 17 Oct 2015
Posts: 30

### Show Tags

15 Jan 2016, 16:33
Hi All!

Could someone please explain how I could solve this exercise without doing the opposite?

Should not the solution be 5/11 X 4/10?

Regards!

Bunuel wrote:
Official Solution:

A box contains 11 hats, out of which 6 are red hats and 5 are green hats. If two hats are to be selected at random without replacement, what is the probability that at least one green hat will be selected?

A. $$\frac{10}{11}$$
B. $$\frac{8}{11}$$
C. $$\frac{7}{12}$$
D. $$\frac{5}{13}$$
E. $$\frac{2}{7}$$

It's easier to find the probability of the opposite event and subtract it from 1. The opposite event would be if we select zero green hats, or which is the same if we select 2 red hats, so: $$P(G \ge 1)=1-P(RR)=1-\frac{6}{11}*\frac{5}{10}=\frac{8}{11}$$.

Math Expert
Joined: 02 Aug 2009
Posts: 5548

### Show Tags

18 Jan 2016, 06:48
2
KUDOS
Expert's post
mestrec wrote:
Hi All!

Could someone please explain how I could solve this exercise without doing the opposite?

Should not the solution be 5/11 X 4/10?

Regards!

Bunuel wrote:
Official Solution:

A box contains 11 hats, out of which 6 are red hats and 5 are green hats. If two hats are to be selected at random without replacement, what is the probability that at least one green hat will be selected?

A. $$\frac{10}{11}$$
B. $$\frac{8}{11}$$
C. $$\frac{7}{12}$$
D. $$\frac{5}{13}$$
E. $$\frac{2}{7}$$

It's easier to find the probability of the opposite event and subtract it from 1. The opposite event would be if we select zero green hats, or which is the same if we select 2 red hats, so: $$P(G \ge 1)=1-P(RR)=1-\frac{6}{11}*\frac{5}{10}=\frac{8}{11}$$.

Hi,
although you should solve by looking at the prob of opposite event, since it is less time consuming and less error prone..
the normal way would be..
there are 5 green and 6 red ...
so way you can pick up atleast one of red is..
both green=$$\frac{5}{11}*\frac{4}{10}$$..
one red and one green=$$\frac{6}{11}*\frac{5}{10}$$ and $$\frac{5}{11}*\frac{6}{10}$$ (2 ways one of each can be picked up)
total prob=$$\frac{5}{11}*\frac{4}{10} + \frac{6}{11} * \frac{5}{10} *2= \frac{(20+60)}{110}= \frac{8}{11}$$
hope it helps you
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Intern
Joined: 30 May 2013
Posts: 29
GMAT 1: 600 Q50 V21

### Show Tags

26 Jun 2017, 08:17
1
KUDOS
1
This post was
BOOKMARKED
Total Cases : 11C2 = 55
Prob. of Picking up One Green Hat = 5c1 * 6c1 = 30 (One from Green Hat Box and Other from Red Hat Box)
Prob. of Picking up Two Green Hat = 5c2 = 10 (Both from Green Hat Bucket)

P(x) = (30 + 10)/55
= 40/55 = 8/11
Intern
Joined: 20 Sep 2016
Posts: 26

### Show Tags

17 Nov 2017, 10:06
I am not sure what am i doing wrong in the problem? my approach is :
1 red and one green or both green
thus, (6/11*5/10) or (5/11*4/10)
=5/11

Math Expert
Joined: 02 Aug 2009
Posts: 5548

### Show Tags

17 Nov 2017, 10:19
1
KUDOS
Expert's post
jyotipes21@gmail.com wrote:
I am not sure what am i doing wrong in the problem? my approach is :
1 red and one green or both green
thus, (6/11*5/10) or (5/11*4/10)
=5/11

Hi..

Where you are going wrong is that you are taking two cases RG and GR as one case..
You can pick green then red OR pick red then green OR pick both green..
So 6/11*5/10+5/12*6/10+5/11*4/10

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Manager
Joined: 02 Jan 2017
Posts: 90
Location: Pakistan
Concentration: Finance, Technology
GMAT 1: 650 Q47 V34
GPA: 3.41

### Show Tags

24 Dec 2017, 03:31
Can anyone explain ( Experts in particular)

Why has the order not matter here? Is it because of the word ( selection) used in Question stem which hints for a Combination question?

Atleast one green will be interpreted as ( Green, Green ) Or ( Green , Red) [ Now this can also be taken as ) --> (Red, Green)

But here we have only take these two ( Green, Green ) Or ( Green , Red) as possibilities and left out the third one. Kindly clarify.
Math Expert
Joined: 02 Aug 2009
Posts: 5548

### Show Tags

24 Dec 2017, 03:38
mtk10 wrote:
Can anyone explain ( Experts in particular)

Why has the order not matter here? Is it because of the word ( selection) used in Question stem which hints for a Combination question?

Atleast one green will be interpreted as ( Green, Green ) Or ( Green , Red) [ Now this can also be taken as ) --> (Red, Green)

But here we have only take these two ( Green, Green ) Or ( Green , Red) as possibilities and left out the third one. Kindly clarify.

Hi..

Here the order matters and you have to take all 3 cases.
See solutions above
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Re: D01-37   [#permalink] 24 Dec 2017, 03:38
Display posts from previous: Sort by

# D01-37

Moderators: chetan2u, Bunuel

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