Last visit was: 23 Apr 2026, 00:15 It is currently 23 Apr 2026, 00:15
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
805+ (Hard)|   Probability|      
User avatar
registerincog
User avatar
Joined: 16 Nov 2013
Last visit: 17 Dec 2014
Posts: 23
Own Kudos:
533
 [46]
Given Kudos: 20
Location: United States
Concentration: Entrepreneurship, General Management
GPA: 3.49
Posts: 23
Kudos: 533
 [46]
From a group of 10 people, a committee of four people is to 20 Nov 2013, 03:12
5
Kudos
Add Kudos
41
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

41% (02:34) correct 59% (02:15) wrong based on 514 sessions

History

Date
Time
Result
Not Attempted Yet
From a group of 10 people, a committee of four people is to randomly formed. Is the probability greater than 50% that the committee will contain more women than men?

(1) The group from which the committee is formed contains more women than men
(2) The ratio of women to men in the group from which the committee is formed is greater than or equal to 3:2
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,763
Own Kudos:
810,709
 [19]
Given Kudos: 105,850
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,763
Kudos: 810,709
 [19]
From a group of 10 people, a committee of four people is to 20 Nov 2013, 03:42
7
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
From a group of 10 people, a committee of four people is to randomly formed. Is the probability greater than 50% that the committee will contain more women than men?

More women than men in 4-person committee means one of the following 2 cases:
WWWW
WWWM

(1) The group from which the committee is formed contains more women than men.

If there are 10 women in the group then the probability of getting more women will obviously be greater than 50% (100%). I
If there are 6 women and 4 men, then \(P(W>M)=\frac{C^4_6}{C^4_{10}}+\frac{C^3_6*C^1_4}{C^4_{10}}=\frac{15}{210}+\frac{20*4}{210}=\frac{95}{210}<\frac{1}{2}\).

Not sufficient.

(2) The ratio of women to men in the group from which the committee is formed is greater than or equal to 3:2 --> \(\frac{W}{M}\geq{\frac{3}{2}}\). We can get two different answers if we consider 9 women and 1 men and 6 women and 4 men. Not sufficient.

(1)+(2) Consider the same examples as above. Not sufficient.

Answer: E.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,763
Own Kudos:
810,709
 [9]
Given Kudos: 105,850
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,763
Kudos: 810,709
 [9]
From a group of 10 people, a committee of four people is to 20 Nov 2013, 03:45
2
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
Bunuel
From a group of 10 people, a committee of four people is to randomly formed. Is the probability greater than 50% that the committee will contain more women than men?

More women than men in 4-person committee means one of the following 2 cases:
WWWW
WWWM

(1) The group from which the committee is formed contains more women than men.

If there are 10 women in the group then the probability of getting more women will obviously be greater than 50% (100%). I
If there are 6 women and 4 men, then \(P(W>M)=\frac{C^4_6}{C^4_{10}}+\frac{C^3_6*C^1_4}{C^4_{10}}=\frac{15}{210}+\frac{20*4}{210}=\frac{95}{210}<\frac{1}{2}\).

Not sufficient.

(2) The ratio of women to men in the group from which the committee is formed is greater than or equal to 3:2 --> \(\frac{W}{M}\geq{\frac{3}{2}}\). We can get two different answers if we consider 9 women and 1 men and 6 women and 4 men. Not sufficient.

(1)+(2) Consider the same examples as above. Not sufficient.

Answer: E.
Show more

Similar questions to practice:
a-committee-consists-of-n-women-and-k-men-in-addition-there-127620.html (700+)
if-2-different-representatives-are-to-be-selected-at-random-128233.html (GMAT Prep 700)
a-committee-of-2-people-is-to-be-formed-from-a-group-of-108096.html (700)
a-certain-panel-is-to-be-composed-of-exactly-three-women-and-108964.html

Hope this helps.
General Discussion
User avatar
HarveyS
User avatar
Joined: 14 Jan 2013
Last visit: 25 Apr 2017
Posts: 112
Own Kudos:
1,765
Given Kudos: 30
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE:Consulting (Consulting)
Posts: 112
Kudos: 1,765
From a group of 10 people, a committee of four people is to 16 Jan 2014, 20:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
From a group of 10 people, a committee of four people is to randomly formed. Is the probability greater than 50% that the committee will contain more women than men?

More women than men in 4-person committee means one of the following 2 cases:
WWWW
WWWM

(1) The group from which the committee is formed contains more women than men.

If there are 10 women in the group then the probability of getting more women will obviously be greater than 50% (100%). I
If there are 6 women and 4 men, then \(P(W>M)=\frac{C^4_6}{C^4_{10}}+\frac{C^3_6*C^1_4}{C^4_{10}}=\frac{15}{210}+\frac{20*4}{210}=\frac{95}{210}<\frac{1}{2}\).

Not sufficient.

(2) The ratio of women to men in the group from which the committee is formed is greater than or equal to 3:2 --> \(\frac{W}{M}\geq{\frac{3}{2}}\). We can get two different answers if we consider 9 women and 1 men and 6 women and 4 men. Not sufficient.

(1)+(2) Consider the same examples as above. Not sufficient.

Answer: E.
Show more

Bunuel,

I am not clear that we you added 6C4 + 6C3x 4C1 in statement 1
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,763
Own Kudos:
810,709
 [2]
Given Kudos: 105,850
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,763
Kudos: 810,709
 [2]
From a group of 10 people, a committee of four people is to 17 Jan 2014, 00:48
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Mountain14
Bunuel
From a group of 10 people, a committee of four people is to randomly formed. Is the probability greater than 50% that the committee will contain more women than men?

More women than men in 4-person committee means one of the following 2 cases:
WWWW
WWWM

(1) The group from which the committee is formed contains more women than men.

If there are 10 women in the group then the probability of getting more women will obviously be greater than 50% (100%). I
If there are 6 women and 4 men, then \(P(W>M)=\frac{C^4_6}{C^4_{10}}+\frac{C^3_6*C^1_4}{C^4_{10}}=\frac{15}{210}+\frac{20*4}{210}=\frac{95}{210}<\frac{1}{2}\).

Not sufficient.

(2) The ratio of women to men in the group from which the committee is formed is greater than or equal to 3:2 --> \(\frac{W}{M}\geq{\frac{3}{2}}\). We can get two different answers if we consider 9 women and 1 men and 6 women and 4 men. Not sufficient.

(1)+(2) Consider the same examples as above. Not sufficient.

Answer: E.

Bunuel,

I am not clear that we you added 6C4 + 6C3x 4C1 in statement 1
Show more

P(W>M) = P(WWWW) + P(WWWM).

If there are 6 women and 4 men, then, then \(P(WWWW)=\frac{C^4_6}{C^4_{10}}\) and \(P(WWWM)=\frac{C^3_6*C^1_4}{C^4_{10}}\).

Hope it's clear.
User avatar
hellosanthosh2k2
User avatar
Joined: 02 Apr 2014
Last visit: 07 Dec 2020
Posts: 360
Own Kudos:
619
Given Kudos: 1,227
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
GPA: 3.5
Schools: XLRI"20
GMAT 1: 700 Q50 V34
Posts: 360
Kudos: 619
From a group of 10 people, a committee of four people is to 20 Nov 2017, 11:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
From a group of 10 people, a committee of four people is to randomly formed. Is the probability greater than 50% that the committee will contain more women than men?

More women than men in 4-person committee means one of the following 2 cases:
WWWW
WWWM

(1) The group from which the committee is formed contains more women than men.

If there are 10 women in the group then the probability of getting more women will obviously be greater than 50% (100%). I
If there are 6 women and 4 men, then \(P(W>M)=\frac{C^4_6}{C^4_{10}}+\frac{C^3_6*C^1_4}{C^4_{10}}=\frac{15}{210}+\frac{20*4}{210}=\frac{95}{210}<\frac{1}{2}\).

Not sufficient.

(2) The ratio of women to men in the group from which the committee is formed is greater than or equal to 3:2 --> \(\frac{W}{M}\geq{\frac{3}{2}}\). We can get two different answers if we consider 9 women and 1 men and 6 women and 4 men. Not sufficient.

(1)+(2) Consider the same examples as above. Not sufficient.

Answer: E.
Show more

Hi Bunuel,

I have one question, are n't both statements saying same thing ?

Statement 1: more women than men => w >= 6 and m <= 4 =>
if w = 6, m = 4, ratio w/m = 3/2
if w = 7, m = 3, ratio w/m = 7/3
ratio w/m >= 3/2

Statement 2: is exactly saying w/m >= 3/2

but answer is definitely (E) as we will get diff probabilities with cases w = 6, m = 4 and w = 7, m = 3 .....

Please clarify

Thanks
User avatar
Balkrishna
User avatar
Joined: 17 Aug 2018
Last visit: 13 May 2022
Posts: 48
Own Kudos:
50
 [2]
Given Kudos: 308
Status:Chartered Accountant
Location: India
WE:Accounting (Consulting)
Posts: 48
Kudos: 50
 [2]
From a group of 10 people, a committee of four people is to 16 Feb 2020, 05:26
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Quick and easy solution without any calculation.

If you have 3 women in the committee of 4 people, ratio of women to men is 3:1.

So, in order to have the probability of more women than men in the committee greater than 0.5, total number of women must be greater than 3/4, i.e. 7.5 out of 10. So, we need at least 8 women in the total population to get the probability higher than 0.5.


Statement-1:
The number of women is higher than number men in the total population.
No. of women > 5.
No. of women may or may not be greater than or equal to 8.

So, statement 1 is not sufficient.

Statement-2:
The number of women is 6 or higher in the total population.
No. of women may or may not be greater than or equal to 8.

So, statement 2 is not sufficient.

Combining both statements:
Even after combining both statements, no. of women may or may not be greater than or equal to 8.

So, ans is E.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,959
Own Kudos:
1,117
Posts: 38,959
Kudos: 1,117
From a group of 10 people, a committee of four people is to 06 Apr 2025, 08:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109763 posts
kingbucky
498 posts
Gmat860sanskar
212 posts