• Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • 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

Probability

This topic has 2 expert replies and 2 member replies
prernamalhotra Senior | Next Rank: 100 Posts Default Avatar
Joined
02 Apr 2014
Posted:
44 messages
Followed by:
1 members
Thanked:
2 times

Probability

Post Mon Jun 16, 2014 6:14 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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?

    1) 1/14
    2) 1/7
    3) 2/7
    4) 3/7
    5) 1/2

    Thank you,
    Prerna

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Mon Jun 16, 2014 6:22 am
    prernamalhotra 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
    One approach is to apply counting methods:

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

    # of teams with exactly 2 women
    Take the task of selecting 2 women and 2 men and break it into stages.
    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.
    By the Fundamental Counting Principle (FCP), the 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 (like 5C2) in your head, you can watch our free video: http://www.gmatprepnow.com/module/gmat-counting?id=789

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course

    Thanked by: prernamalhotra
    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    Mathsbuddy Master | Next Rank: 500 Posts Default Avatar
    Joined
    08 Nov 2013
    Posted:
    447 messages
    Followed by:
    1 members
    Thanked:
    25 times
    Post Mon Jun 16, 2014 6:32 am
    6 combinations each with probability (5*4*3*2)/(8*7*6*5) = 3/7

    Post Mon Jun 16, 2014 7:14 am
    Quote:
    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
    When a probability problem uses the word exactly, we can apply the following reasoning:
    P(exactly n) = P(one way) * all possible ways.

    Let W = woman and M = man.

    P(one way):
    One way to get 2 women and 2 men is WWMM.
    P(1st person is W) = 5/8. (8 people, 5 of them W.)
    P(2nd person is W) = 4/7. (7 people left, 4 of them W.)
    P(3rd person is M) = 3/6. (6 people left, 3 of them M.)
    P(4th person is M) = 2/5. (5 people left, 2 of them M.)
    Since we want all of these events to happen together, we multiply the fractions:
    P(WWMM) = 5/8 * 4/7 * 3/6 * 2/5 = 1/14.

    All possible ways:
    Any arrangement of WWMM will yield exactly 2 W and 2 M.
    Thus, the result above must be multiplied by the number of ways to ARRANGE the 4 elements WWMM.

    The number of ways to arrange 4 elements = 4!.
    But WWMM includes IDENTICAL elements.
    When an arrangement includes identical elements, we must divide by the number of ways each set of identical elements can be arranged.
    The reason:
    When the identical elements swap places, the arrangement DOESN'T CHANGE.
    Here, we must divide by 2! to account for the two identical W's and by another 2! to account for the two identical M's:
    4!/(2!2!) = 6.

    Thus:
    P(exactly 2 W) = 1/14 * 6 = 3/7.

    The correct answer is D.

    _________________
    Mitch Hunt
    GMAT Private Tutor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.

    Thanked by: prernamalhotra
    Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
    GMATinsight Legendary Member
    Joined
    10 May 2014
    Posted:
    998 messages
    Followed by:
    21 members
    Thanked:
    203 times
    Post Mon Jun 16, 2014 7:56 am
    The answer will staraight away be this way

    Probability = (favorable outcome) / (Total Outcome)
    = (3C2 x 5C2)/(8C4) = 30/70 = 3/7 ANSWER

    [ 3C2 refers the no. of ways of selecting 2 men out of 3 men and 5C2 refers the number of ways of selecting 2 Women out of 5 Women ]

    [8C4 refers to the total number of ways of selecting 4 out of 8 individuals]

    _________________
    Prosper!!!
    Bhoopendra Singh & Sushma Jha
    "GMATinsight"
    Contact Us
    Testimonials
    To register for One-on-One FREE ONLINE DEMO Class Call/e-mail
    e-mail: info@GMATinsight.com
    Mobile: +91-9999687183 / +91-9891333772
    Get in touch for SKYPE-Based Interactive Private Tutoring
    One-On-One Classes fee - US$40 per hour &
    for FULL COURSE (38 LIVE Sessions)-US$1000

    "Please click on 'Thank' if you like my post/response."

    Classroom Centres Address:
    GMATinsight
    Dwarka, New Delhi-110075 and Shivalik New Delhi

    Best Conversation Starters

    1 Vincen 180 topics
    2 lheiannie07 61 topics
    3 Roland2rule 61 topics
    4 ardz24 40 topics
    5 VJesus12 14 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    160 posts
    2 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    102 posts
    3 image description GMATGuruNY

    The Princeton Review Teacher

    99 posts
    4 image description Jay@ManhattanReview

    Manhattan Review

    86 posts
    5 image description Matt@VeritasPrep

    Veritas Prep

    80 posts
    See More Top Beat The GMAT Experts