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

 It is currently 04 May 2015, 16:31

### 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

# 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
Status: The last round
Joined: 18 Jun 2009
Posts: 1317
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 64

Kudos [?]: 592 [0], given: 157

Probability; Equal number of boys & girls [#permalink]  06 Jul 2010, 09:49
00:00

Difficulty:

(N/A)

Question Stats:

56% (01:33) correct 44% (01:02) wrong based on 21 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
_________________
Intern
Joined: 02 Jun 2010
Posts: 29
Followers: 0

Kudos [?]: 2 [0], given: 4

Re: Probability; Equal number of boys & girls [#permalink]  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
Joined: 02 Jun 2010
Posts: 29
Followers: 0

Kudos [?]: 2 [0], given: 4

Re: Probability; Equal number of boys & girls [#permalink]  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)
Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1923
Concentration: General Management, Nonprofit
Followers: 380

Kudos [?]: 1550 [0], given: 210

Re: Probability; Equal number of boys & girls [#permalink]  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
Joined: 21 Feb 2010
Posts: 214
Followers: 1

Kudos [?]: 16 [0], given: 1

Re: Probability; Equal number of boys & girls [#permalink]  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
Status: The last round
Joined: 18 Jun 2009
Posts: 1317
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 64

Kudos [?]: 592 [0], given: 157

Re: Probability; Equal number of boys & girls [#permalink]  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.
_________________
Re: Probability; Equal number of boys & girls   [#permalink] 08 Jul 2010, 23:56
Similar topics Replies Last post
Similar
Topics:
5 A class contains boys and girls. What is the probability of selecting 8 18 Feb 2015, 03:52
The ratio of the number of boys to the number of girls in Wa 2 03 Mar 2014, 06:48
Boys to Girls Ratio 2 06 May 2010, 14:35
4 If there is an equal probability of a child being born a boy 9 07 Sep 2009, 09:09
permutations boys and girl 7 10 Aug 2006, 17:27
Display posts from previous: Sort by

# Probability; Equal number of boys & girls

 Question banks Downloads My Bookmarks Reviews Important topics

 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®.