• 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

Two thirds of the roads from A to B are at least 5 miles

This topic has 3 expert replies and 0 member replies

Two thirds of the roads from A to B are at least 5 miles

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Two thirds of the roads from A to B are at least 5 miles long, and 1/4 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?
(A) 1/6
(B) 1/4
(C) 2/3
(D) 3/4
(E) 11/12

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Top Reply
Post
BTGmoderatorDC wrote:
Two thirds of the roads from A to B are at least 5 miles long, and 1/4 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?
(A) 1/6
(B) 1/4
(C) 2/3
(D) 3/4
(E) 11/12
The only way that you won’t pick a road that is at least 5 miles long is if you pick a road from A to B that is less than 5 miles long and you also pick a road from B to C that is less than 5 miles long. The probability of the former is ", and the probability of the latter is 3/4. Therefore, the probability of picking no roads that are at least 5 miles long is 1/3 x 3/4 = 1/4. In other words, the probability of picking at least one road that is at least 5 miles long is 1 - 1/4 = 3/4.

Answer: D

_________________
Jeffrey Miller Head of GMAT Instruction

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Top Reply
Post
Hi All,

We're told that 2/3 of the roads from A to B are at least 5 miles long, and 1/4 of the roads from B to C are at least 5 miles long. We're asked if you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that AT LEAST one of the roads you pick is at least 5 miles long.

In these types of probability questions, it's often easiest to calculate the probability of what you DON'T WANT (and then subtract that from 1 to get the probability of what you DO want); Mitch's approach showcased that math. You can calculate the various ways to 'fit' what you DO want though - although it will be a bit more work (and in certain questions, it would be a lot more work).

There would be 3 ways for AT LEAST one of the two roads being at least 5 miles long:
1) First road IS, second road ISN'T
2) First road ISN'T, second road IS
3) Both roads ARE

The individual probabilities of those three events are:
1) (2/3)(3/4) = 6/12
2) (1/3)(1/4) = 1/12
3) (2/3)(1/4) = 2/12
Total probability = 6/12 + 1 /12 + 2/12 = 9/12 = 3/4

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
BTGmoderatorDC wrote:
Two thirds of the roads from A to B are at least 5 miles long, and 1/4 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?
(A) 1/6
(B) 1/4
(C) 2/3
(D) 3/4
(E) 11/12
P(at least one of the 2 selected roads is at least 5 miles long) = 1 - P(neither of the 2 selected roads is at least 5 miles long)

From A to B:
Since 2/3 of the roads are at least 5 miles long, 1/3 are not.
Thus, the probability of selecting a road that is not at least 5 miles long = 1/3.

From B to C:
Since 1/4 of the roads are at least 5 miles long, 3/4 are not.
Thus, the probability of selecting a road that is not at least 5 miles long = 3/4.

P(neither of the 2 selected roads is at least 5 miles long) = (1/3)(3/4) = 1/4.
Thus:
P(at least one of the 2 selected roads is at least 5 miles long) = 1 - 1/4 = 3/4.

The correct answer is D.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
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.
  • 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
  • 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
  • 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
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider

Top First Responders*

1 GMATGuruNY 56 first replies
2 Brent@GMATPrepNow 43 first replies
3 Jay@ManhattanReview 43 first replies
4 Ian Stewart 31 first replies
5 ceilidh.erickson 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

217 posts
2 image description fskilnik@GMATH

GMATH Teacher

124 posts
3 image description Max@Math Revolution

Math Revolution

89 posts
4 image description GMATGuruNY

The Princeton Review Teacher

82 posts
5 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

66 posts
See More Top Beat The GMAT Experts