• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 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

In a certain game only one player can win and only one

This topic has 1 expert reply and 0 member replies

In a certain game only one player can win and only one

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Manhattan Prep

In a certain game only one player can win and only one player always eventually wins. James, Austin, and Katelyn play this game together 3 times in a row. What is the probability that Katelyn wins at least one of the 3 games?

1) The probability that either James or Austin wins the game is 3/4.
2) James and Katelyn have an equal probability of winning the game.

OA A

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
AAPL wrote:
Manhattan Prep

In a certain game only one player can win and only one player always eventually wins. James, Austin, and Katelyn play this game together 3 times in a row. What is the probability that Katelyn wins at least one of the 3 games?

1) The probability that either James or Austin wins the game is 3/4.
2) James and Katelyn have an equal probability of winning the game.

OA A
Target question: What is the probability that Katelyn wins at least one of the 3 games?
This is a good candidate for rephrasing the target question.
In order to determine P(Katelyn wins at least one of the 3 games), we need to know the probability that Katelyn wins if they play ONE game.
We can then use that information to determine the probability of her winning at least one of 3 games

REPHRASED target question: What is the probability that Katelyn wins if they play ONE game?

Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Statement 1: The probability that either James or Austin wins the game is 3/4.
Use the complement to write: P(Katelyn wins) = 1 - P(Katelyn DOESN'T win)
Notice that, if Katelyn DOESN'T win, then EITHER James wins OR Austin wins
In other words, P(Katelyn DOESN'T win) = P(James wins or Austin wins)
Statement 1 tells us that P(James wins or Austin wins) = 3/4
So, P(Katelyn DOESN'T win) = 3/4
So, P(Katelyn wins) = 1 - 3/4 = 1/4
So, the answer to the REPHRASED target question is P(Katelyn wins) = 1/4
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: James and Katelyn have an equal probability of winning the game.
Key Concept: If the 3 people play one game, then P(James wins) + P(Austin wins) + P(Katelyn wins) = 1
There are infinitely many scenarios that satisfy statement 2. Here are two:
Case a: P(James wins a game) = 0.3, P(Katelyn wins a game) = 0.3 and P(Austin wins a game) = 0.4 . In this case, the answer to the REPHRASED target question is P(Katelyn wins) = 0.3
Case b: P(James wins a game) = 0.2, P(Katelyn wins a game) = 0.2 and P(Austin wins a game) = 0.6 . In this case, the answer to the REPHRASED target question is P(Katelyn wins) = 0.2
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

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

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
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!
  • 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
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • 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

Top First Responders*

1 Brent@GMATPrepNow 39 first replies
2 Ian Stewart 37 first replies
3 Jay@ManhattanReview 32 first replies
4 GMATGuruNY 26 first replies
5 Scott@TargetTestPrep 15 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 Scott@TargetTestPrep

Target Test Prep

199 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

71 posts
4 image description GMATGuruNY

The Princeton Review Teacher

45 posts
5 image description Ian Stewart

GMATiX Teacher

43 posts
See More Top Beat The GMAT Experts