Probability

Expert replies

sparkle6: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Tue Sep 20, 2011 7:58 amFollowed by: 1 member; Thanked: 1 times

by sparkle6 » Mon Oct 03, 2011 6:43 am

A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

a. 1/14

b. 1/7

c. 2/7

d. 3/7

e. 1/2

[spoiler]Answer: D. Can someone explain with combinations?[/spoiler]

Like this post

Source: Beat The GMAT — Problem Solving | Mon Oct 03, 2011 6:43 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Oct 03, 2011 6:50 am

Selecting 2 women and 2 men

5/8 * 4/7 * 3/6 * 2/5 (First 2 are girls and next 2 are boys)

Now these 4 can be arranged in 4!/2!2! ways

So to consider all arrangements, multiply

5/8 * 4/7 * 3/6 * 2/5 * 4!/2!2! = 3/7

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Oct 03, 2011 6:57 am

sparkle6 wrote:A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

a. 1/14
b. 1/7
c. 2/7
d. 3/7
e. 1/2

[spoiler]Answer: D. Can someone explain with combinations?[/spoiler]

Solution via counting methods:

P(exactly 2 women) = [# of teams with exactly 2 women] / [total # of teams possible]

# of teams with exactly 2 women
Stage 1: Select 2 women for the team. There are 5 women to choose from, so this can be accomplished in 5C2 ways.
Stage 2: Select 2 men for the team. There are 3 men to choose from, so this can be accomplished in 3C2 ways.

Total number of teams with exactly 2 women = (5C2)(3C2) = (10)(3) = 30

# of teams possible
There are 8 people altogether and we must choose 4 of them.
This can be accomplished in 8C4 ways, which equals 70 ways

P(exactly 2 women) = [30] / [70]
= 3/7 = D

Aside: To learn how to calculate combinations such as 5C2 in your head, you can watch video #17 at https://www.gmatprepnow.com/module/gmat-counting (it's free)
Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review