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

It is currently 19 Dec 2014, 13:40

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

Probability; Equal number of boys & girls

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1317
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 62

Kudos [?]: 522 [0], given: 157

GMAT ToolKit User
Probability; Equal number of boys & girls [#permalink] New post 06 Jul 2010, 09:49
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

36% (01:13) correct 64% (01:02) wrong based on 11 sessions
From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the
probability that equal numbers of boys and girls will be selected?

A.1/10
B.4/9
C.1/2
D.3/5
E.2/3
_________________

[ From 470 to 680-My Story ] [ My Last Month Before Test ]
[ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]

I Can, I Will

Intern
Intern
avatar
Joined: 02 Jun 2010
Posts: 29
Followers: 0

Kudos [?]: 1 [0], given: 4

GMAT ToolKit User
Re: Probability; Equal number of boys & girls [#permalink] New post 06 Jul 2010, 11:06
Hussain15 wrote:
From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the
probability that equal numbers of boys and girls will be selected?

A.1/10
B.4/9
C.1/2
D.3/5
E.2/3



So we are asked - what is probability of selecting 2 boys and 2 girls right:

We were not told about the actual selection, hence Before finding the probability, we should find what the different ways in which we can select 4 children.
So select 1 boy, then 1 boy, then 1 girl and then 1 girl or you can also select 1 B, 1 G, 1 B and 1 G.
Basically selecting 4 from BBGG. ie. 4 * 3 * 2 *1 / (2! * 2!) ways of making the selection. = 6.

Probability of selecting 1st boy = 3/6
Probability of selecting 2nd boy = 2/5 (as we have already selected one boy above)
Probability of selecting 1st Girl = 3/4
Probability of selecting 2nd Girl = 2/3

Multiply all of above with different ways of selecting the children =
P (selecting 2 boys and 2 girls) = 3/6 * 2/5 * 3/4 * 2/3 * 6 = 3/5

Answer : D
Intern
Intern
avatar
Joined: 02 Jun 2010
Posts: 29
Followers: 0

Kudos [?]: 1 [0], given: 4

GMAT ToolKit User
Re: Probability; Equal number of boys & girls [#permalink] New post 06 Jul 2010, 12:34
surjoy wrote:
Hussain15 wrote:
From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the
probability that equal numbers of boys and girls will be selected?

A.1/10
B.4/9
C.1/2
D.3/5
E.2/3



So we are asked - what is probability of selecting 2 boys and 2 girls right:

We were not told about the actual selection, hence Before finding the probability, we should find what the different ways in which we can select 4 children.
So select 1 boy, then 1 boy, then 1 girl and then 1 girl or you can also select 1 B, 1 G, 1 B and 1 G.
Basically selecting 4 from BBGG. ie. 4 * 3 * 2 *1 / (2! * 2!) ways of making the selection. = 6.

Probability of selecting 1st boy = 3/6
Probability of selecting 2nd boy = 2/5 (as we have already selected one boy above)
Probability of selecting 1st Girl = 3/4
Probability of selecting 2nd Girl = 2/3

Multiply all of above with different ways of selecting the children =
P (selecting 2 boys and 2 girls) = 3/6 * 2/5 * 3/4 * 2/3 * 6 = 3/5

Answer : D


There is actually much simpler approach for this problem.

P (selecting 2 boys and 2 girls) = (No. of ways of selecting 2 boys out of 3 * no. of ways of selecting 2 girls out of 3) / Total ways of selecting 4 out of 6 children
= 3C2 * 3C2 / 6C4 = 3/5 (D)
Expert Post
Ms. Big Fat Panda
Ms. Big Fat Panda
User avatar
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1918
Concentration: Social Entrepreneurship, Organizational Behavior
Followers: 361

Kudos [?]: 1476 [0], given: 209

GMAT ToolKit User
Re: Probability; Equal number of boys & girls [#permalink] New post 06 Jul 2010, 12:41
Expert's post
Fairly straightforward question I think.

Ways to select 2 boys out of 3 = 3C2 = Ways to select 2 girls out of 3

Total ways to select 4 children = 6C4

So probability = \frac{3C2*3C2}{6C4} = \frac{3}{5}

Hope this helps!
Manager
Manager
avatar
Joined: 21 Feb 2010
Posts: 214
Followers: 1

Kudos [?]: 13 [0], given: 1

Re: Probability; Equal number of boys & girls [#permalink] New post 06 Jul 2010, 13:11
any bible for the GMAT probability and combination? i read the MGMAT, it helps a little...any better books out there?
Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1317
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 62

Kudos [?]: 522 [0], given: 157

GMAT ToolKit User
Re: Probability; Equal number of boys & girls [#permalink] New post 08 Jul 2010, 23:56
tt11234 wrote:
any bible for the GMAT probability and combination? i read the MGMAT, it helps a little...any better books out there?


Probability & Combination questions are not so common in GMAT. Hardly one can see 2 or max 3. So try to give your valuable time to the remaining 98% area of GMAT Quantative section. The concepts covered in MGMAT probability section are sufficient to answer a normal GMAT question. If you will go for a bible of GMAT probability, you will merely waste your time. So use this time to cover the topics which are most common in GMAT like number properties, Word problems & inequalities.

Best of luck.
_________________

[ From 470 to 680-My Story ] [ My Last Month Before Test ]
[ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]

I Can, I Will

Re: Probability; Equal number of boys & girls   [#permalink] 08 Jul 2010, 23:56
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic The ratio of the number of boys to the number of girls in Wa dennis14 2 03 Mar 2014, 06:48
Boys to Girls Ratio zisis 2 06 May 2010, 14:35
4 If there is an equal probability of a child being born a boy marcodonzelli 9 07 Sep 2009, 09:09
permutations boys and girl mand-y 7 10 Aug 2006, 17:27
Find the numbers of ways in which 4 boys and 4 girls can be anirban16 9 19 Apr 2005, 17:23
Display posts from previous: Sort by

Probability; Equal number of boys & girls

  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®.