• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

When 2 people are selected at random from a group of 4 femal

This topic has 2 expert replies and 1 member reply

GMAT/MBA Expert

When 2 people are selected at random from a group of 4 femal

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



[Math Revolution GMAT math practice question]

When 2 people are selected at random from a group of 4 females and 4 males, what is the probability that at least one female is selected?

A. 5/14
B. 7/14
C. 9/14
D. 11/14
E. 13/14

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $99 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag
Post
Total possibilities 8c2 = (8*7)/2 = 28.

Now, since we are interested in probability at least one is female, we can find the probability that all 2 are males 4c2 = (4*3)/2 = 6.

Now 6/28 = 3/14.

The probability of at least one female = 1 - (3/14) = 11/14.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Legendary Member
Joined
24 Jul 2015
Posted:
1677 messages
Followed by:
28 members
Upvotes:
19
GMAT Score:
Most Active Expert
Post
=>
The probability that at least one female is selected is equal to 1 minus the probability that two males are selected.
There are 4C2 ways of selecting 2 males from the four males and 8C2 ways of selecting 2 people from the group of 8. Therefore, the probability of selecting two males from the group is 4C2/8C2, and the probability of selecting at least one female is
1 - 4C2/8C2 = 1 - { (4*3)/(1*2) } / { (8*7)/(1*2) } = 1 - (4*3)/(8*7) = 1 - 3/14 = 11/14

Therefore, the answer is D.
Answer: D

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $99 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag
Post
Max@Math Revolution wrote:
When 2 people are selected at random from a group of 4 females and 4 males, what is the probability that at least one female is selected?

A. 5/14
B. 7/14
C. 9/14
D. 11/14
E. 13/14
We can use the formula:

P(at least one female is selected) = 1 - P(no females are selected)

P(no females are selected) = 4/8 x 3/7 = 1/2 x 3/7 = 3/14

P(at least one female is selected) = 1 - 3/14 = 11/14.

Alternate Solution:

Without any restriction, there are 8C2 = 8!/(2!*6!) = 28 different ways to choose two people from a group of eight.

We use the following formula:

#ways to choose two people = #ways where at least one female is selected + #ways where no female is selected

Notice that since there are 4 men, there are 4C2 = 4!/(2!*2!) = 6 ways to choose two people where no female is selected. Thus, 28 - 6 = 22 of the choices include at least one female. Thus, the probability that at least one female is selected is 22/28 = 11/14.

Answer: D

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT

Top First Responders*

1 fskilnik@GMATH 72 first replies
2 Brent@GMATPrepNow 46 first replies
3 Jay@ManhattanReview 44 first replies
4 GMATGuruNY 41 first replies
5 Rich.C@EMPOWERgma... 36 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

192 posts
2 image description Scott@TargetTestPrep

Target Test Prep

183 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

120 posts
4 image description GMATGuruNY

The Princeton Review Teacher

89 posts
5 image description Max@Math Revolution

Math Revolution

87 posts
See More Top Beat The GMAT Experts