BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Probability Question

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Mon Feb 28, 2011 4:16 pm
by yuvarajait » Sat Apr 16, 2011 10:56 pm
A medical researcher must choose one of 14 patients to receive an experimental
medicine called Progaine. The researcher must then choose one of
the remaining 13 patients to receive another medicine, called Ropecia.
Finally, the researcher administers a placebo to one of the remaining 12
patients. All choices are equally random. If Donald is one of the 14 patients,
what is the probability that Donald receives either Progaine or Ropecia?

The answer given is 1/14+1/14 = 1/7, which i feel as incorrect, since the chances of getting ropecia is only 1/13. Could anyone help understanding this. Thanks!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 436
Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members
Thanked: 72 times

by manpsingh87 » Sun Apr 17, 2011 12:37 am
yuvarajait wrote:A medical researcher must choose one of 14 patients to receive an experimental
medicine called Progaine. The researcher must then choose one of
the remaining 13 patients to receive another medicine, called Ropecia.
Finally, the researcher administers a placebo to one of the remaining 12
patients. All choices are equally random. If Donald is one of the 14 patients,
what is the probability that Donald receives either Progaine or Ropecia?

The answer given is 1/14+1/14 = 1/7, which i feel as incorrect, since the chances of getting ropecia is only 1/13. Could anyone help understanding this. Thanks!
well my advice is don't get confused with the wording,each patient has an equal chance of being selected for any of the three experimental medicine..!!!
O Excellence... my search for you is on... you can be far.. but not beyond my reach!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1101
Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members
Thanked: 47 times
GMAT Score:640

by HSPA » Sun Apr 17, 2011 12:48 am
A) selected first = 1/14
B) getting selected for the second = 13/14* 1/13 = 1/14
Here 13/14 stands for not getting selected for first medicine Progaine and the next 1/13 is getting selected for Ropecia.

P(AUB) = P(A) + P(B) = 1/14+ 1/14 = 1/7
First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
Regards,
HSPA.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Sun Apr 17, 2011 6:59 am
yuvarajait wrote:A medical researcher must choose one of 14 patients to receive an experimental
medicine called Progaine. The researcher must then choose one of
the remaining 13 patients to receive another medicine, called Ropecia.
Finally, the researcher administers a placebo to one of the remaining 12
patients. All choices are equally random. If Donald is one of the 14 patients,
what is the probability that Donald receives either Progaine or Ropecia?

The answer given is 1/14+1/14 = 1/7, which i feel as incorrect, since the chances of getting ropecia is only 1/13. Could anyone help understanding this. Thanks!
You can also solve the question using the complement.
P(Progaine or Ropecia) = 1 - P(neither Progaine nor Ropecia)

P(neither Progaine nor Ropecia) = P(not getting selected for Progaine AND not getting selected for Ropecia)
= P(not getting selected for Progaine) x P(not getting selected for Ropecia)
= (13/14) x (12/13)
= 12/14
= 6/7

So, P(Progaine or Ropecia) = 1 - P(neither Progaine nor Ropecia)
= 1 - 6/7
= 1/7
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members
Location: Montreal
Thanked: 1090 times
GMAT Score:780

by Ian Stewart » Sun Apr 17, 2011 11:13 am
yuvarajait wrote:A medical researcher must choose one of 14 patients to receive an experimental
medicine called Progaine. The researcher must then choose one of
the remaining 13 patients to receive another medicine, called Ropecia.
Finally, the researcher administers a placebo to one of the remaining 12
patients. All choices are equally random. If Donald is one of the 14 patients,
what is the probability that Donald receives either Progaine or Ropecia?

The answer given is 1/14+1/14 = 1/7, which i feel as incorrect, since the chances of getting ropecia is only 1/13. Could anyone help understanding this. Thanks!
I posted about a similar problem a moment ago, but you can also just imagine lining up your 14 people, giving the 1st person in line Progaine, the 2nd person Ropecia, and the 3rd person the placebo. The question then becomes 'if you line up 14 people, including Don, what is the probability Don is one of the first 2 people in line?' There are 14 places to put Don, 2 of which are in the first two positions in line, so the answer is 2/14 = 1/7.

Note that the chance of getting Ropecia is *not* 1/13; it is still 1/14. It is only 1/13 if you *know* you were not selected to receive Progaine.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1