• 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

Bag of coins

This topic has 3 expert replies and 0 member replies

Bag of coins

Post
A bag contains 3 gold coins and 7 silver coins. The bag contains nothing else. If 3 coins are selected at random and without replacement from the bag, what is the probability that exactly 2 of the coins are silver?

A) 7/40

B) 7/24

C) 3/10

D) 21/40

E) 2/3

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor
Joined
11 Apr 2010
Posted:
1179 messages
Followed by:
88 members
Upvotes:
447
Post
Probability that exactly 2 coins are silver means the third coin will be gold coin. So, there will be 1 gold coin and 2 silver coins.
Hence, the required probability =

So, the probability that exactly 2 of the coins are silver is 21/40.

The correct answer is (D).

_________________
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor Default Avatar
Joined
19 Oct 2009
Posted:
1302 messages
Followed by:
162 members
Upvotes:
539
GMAT Score:
800
Post
Note that Rahul is using:

Probability = #desirable/#total

in which the denominator is "all the ways we can 'pull out' three coins from ten", and in which the numerator is "all the ways we can pull out 2 silver coins from 7 AND 1 gold coin from 3".

The question could also have been worded "If 3 coins are selected randomly one after another without replacement..." (If you're not replacing them, it doesn't matter whether you pull the three coins out simultaneously or one after another).

_____

We could have also solved by considering order. We want 2 silver and 1 gold, so:

(3/10)*(7/9)*(6/8) = 7/40
(G).........(S).....(S)

Because there are three arrangements in which we can have 2 silver and 1 gold (SSG, GSS, SGS), we have:

3*(7/40) = 21/40

_________________
Kaplan Teacher in Toronto

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test under Proctored Conditions! - Find a practice test near you or live and online in Kaplan's Classroom Anywhere environment. Register today!
Post
pkw209 wrote:
A bag contains 3 gold coins and 7 silver coins. The bag contains nothing else. If 3 coins are selected at random and without replacement from the bag, what is the probability that exactly 2 of the coins are silver?

A) 7/40

B) 7/24

C) 3/10

D) 21/40

E) 2/3
The number of ways to select 2 silver coins is 7C2 = (7 x 6)/2! = 21.

The number of ways to select 1 gold coin is 3C1 =3.

The number of ways to select 3 coins is 10C3 = (10 x 9 x 8)/3! = (10 x 9 x 8)/(3 x 2 x 1) = 10 x 3 x 4 = 120.

So the probability is (21 x 3)/120 = 63/120 = 21/40.

Alternate Solution:

There are 3 different ways to select exactly 2 silver and 1 gold coin, without replacement, out of the coins in the bag. The outcomes are: (GSS) or (SGS) or (SSG).

The probability of GSS is 3/10 x 7/9 x 6/8 = 21/120.

The probability of SGS is 7/10 x 3/9 x 6/8 = 21/120.

The probability of SSG is 7/10 x 6/9 x 3/8 = 21/120.

Thus, the probability of drawing exactly 2 silver and 1 gold coin is 21/120 x 3 = 63/120 = 21/40.

Answer: D

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • 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
  • 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
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep

Top First Responders*

1 fskilnik@GMATH 74 first replies
2 Jay@ManhattanReview 49 first replies
3 Brent@GMATPrepNow 47 first replies
4 GMATGuruNY 43 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

195 posts
2 image description Scott@TargetTestPrep

Target Test Prep

183 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

123 posts
4 image description Max@Math Revolution

Math Revolution

89 posts
5 image description GMATGuruNY

The Princeton Review Teacher

87 posts
See More Top Beat The GMAT Experts