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

Redeem

Ropecia

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 142
Joined: Sun Jun 12, 2011 7:55 am
Thanked: 5 times
Followed by:3 members

Ropecia

by metallicafan » Tue Jan 22, 2013 8:15 am
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?

MGMAT's approach:

"Since Progaine is only administered to one patient, each patient (including Donald) must have probability 1/14 of receiving it. The same logic also holds for Ropecia. Since Donald cannot receive both of the medicines, the desired probability is the probability of receiving Progaine, plus the probability of receiving Ropecia:

1/14 + 1/14 = 1/7 That's the answer.

I don't understand the approach of the MGMAT guys.
In the case of Ropecia, why the probability is 1/14? I think it should be 1/13 because when we give Ropecia there are only 13 patients, not 14. Remember that Ropecia is given after Progaine.

Thanks!
Top
Source: — Problem Solving |

GMAT/MBA Expert

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

by Brent@GMATPrepNow » Tue Jan 22, 2013 8:27 am
metallicafan 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?
I'd probably solve this one by using the complement.

P(Donald receives either Progaine or Ropecia) = 1 - P(Donald receives neither Progaine nor Ropecia)

P(Donald receives neither Progaine nor Ropecia)
At this point, I like to ask, " What exactly must occur in order for this event to happen?"
Well, for Donald to receive neither Progaine nor Ropecia it must be the case that he does not receive Prograine during the first selection and he does not receive Ropecia during the second selection.

In other words, . . .
P(Donald receives neither Progaine nor Ropecia) = P(Donald does not receive Prograine during the 1st selection AND he does not receive Ropecia during the 2nd selection.
= P(Donald does not receive Prograine during the 1st selection) x P(Donald does not receive Ropecia during the 2nd selection)
= (13/14)x(12/13)
= 12/14
= 6/7

So, P(Donald receives either Progaine or Ropecia) = 1 - (6/7)
= [spoiler]1/7[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

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

by Brent@GMATPrepNow » Tue Jan 22, 2013 8:35 am
metallicafan wrote:
I don't understand the approach of the MGMAT guys.
In the case of Ropecia, why the probability is 1/14? I think it should be 1/13 because when we give Ropecia there are only 13 patients, not 14. Remember that Ropecia is given after Progaine.

Think of it this way.

You and 13 friends place 14 balls in a box. The balls are numbered 1 to 14.
All 14 of you will select 1 ball each (without replacement).
The person who selects the ball with #7 on it wins a boat, and the person who selects the ball with #10 on it wins a car.
What is the probability that you win the car?
The probability is 1/14
Does it matter whether you select 1st, 2nd, 3rd or even last?
No, the probability is 1/14

Similarly, the probability is 1/14 that you'll win the boat.
Once again, it doesn't matter whether you select 1st, 2nd, 3rd or even last.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Tue Jan 22, 2013 8:43 am
metallicafan 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?
Of the 14 people, exactly 1 must receive Prograine.
Each person has an EQUAL chance of being selected.
Thus, the probability that DONALD is selected = 1/14.

Of the 14 people, exactly 1 must receive Ropecia.
Each person has an EQUAL chance of being selected.
Thus, the probability that DONALD is selected = 1/14.

Since either outcome is favorable, we ADD the fractions:
1/14 + 1/14 = 2/14 = 1/7.

Check here for a similar problem:
https://www.beatthegmat.com/board-of-dir ... 98739.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top

GMAT/MBA Expert

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

by Brent@GMATPrepNow » Tue Jan 22, 2013 8:49 am
metallicafan 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?
We can also solve the question using counting techniques.

P(Donald receives either Progaine or Ropecia) = 1 - P(Donald receives neither Progaine nor Ropecia)

P(Donald receives neither Progaine nor Ropecia)
P(Donald receives neither medicine) = [total number of ways to make first 2 selections without selecting Donald]/[total number of ways to make first 2 selections]

Always begin with the denominator.
total number of ways to make first 2 selections
There are 14 ways to select the 1st person.
There are 13 ways to select the 2nd person.
So, by the Fundamental Counting Principle (FCP) we can select the two people in (14)(13) ways

total number of ways to make first 2 selections without selecting Donald
How do we ensure that Donald is not selected?
Remove him from the group entirely. This leaves 13 people from which to make the first 2 selections.
There are 13 ways to select the 1st person.
There are 12 ways to select the 2nd person.
By the Fundamental Counting Principle (FCP) we can select the two people in (13)(12) ways


So, P(Donald receives neither medicine) = (13)(12)/(14)(13)
= 6/7

So, P(Donald receives either Progaine or Ropecia) = 1 - (6/7)
= [spoiler]1/7[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Senior | Next Rank: 100 Posts
Posts: 48
Joined: Thu Jan 19, 2012 10:16 pm
Thanked: 2 times

by whats_in_the_store » Wed Jan 23, 2013 7:32 am
Though the experts have nailed it, I'll try to put my reasoning procedure (which is more or less the same):

P(D getting P)= 1/14
We'll stop here.

P(D not getting P) = 13/14
Next P(D getting R) = 1/13
So, thus P becomes 13/14 * 1/13 = 1/14

So, overall P(D getting either a P or a R ) = 1/14 + 1/14 = 1/7

Hope it helps!
Top

GMAT/MBA Expert

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

by Brent@GMATPrepNow » Wed Jan 23, 2013 7:42 am
metallicafan wrote: I don't understand the approach of the MGMAT guys.
In the case of Ropecia, why the probability is 1/14? I think it should be 1/13 because when we give Ropecia there are only 13 patients, not 14. Remember that Ropecia is given after Progaine.
Thanks!
Here's another way to look at it.
What if, instead of giving Ropecia to the 2nd chosen person, the researcher gives Ropecia to the 14th chosen person.
Using your logic, the probability that Donald gets Ropecia would be 1/1 (100%) since there's only one person left at that point. Of course, the probability isn't 100% because it's quite possible that Donald is selected well before the 14th person. So, we need to also factor in the probability that Donald is not selected earlier.

So, P(Donald is selected 2nd) = P(Donald is not selected 1st AND Donald is selected 2nd)
= P(Donald is not selected 1st) x P(Donald is selected 2nd)
= 13/14 x 1/13
= 1/14

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Senior | Next Rank: 100 Posts
Posts: 87
Joined: Mon May 07, 2012 7:57 am
Thanked: 1 times

by mparakala » Sun Jan 27, 2013 9:47 am
getting selected for Progaine (the 1st time) = 1/14

(or)

NOT getting selected for Progaine AND getting selected for Ropecia (the 2nd time) = 13/14 * 1/13 = 1/14

1/14 + 1/14 = 2/14 = 1/7
Top
Post new topic Post Reply
• Page 1 of 1