Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 18 08:00 AM PDT  09:00 AM PDT Learn an intuitive, systematic approach that will maximize your success on Fillintheblank GMAT CR Questions. Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss!
Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1002
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs

A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
11 Feb 2012, 18:37
Question Stats:
78% (00:57) correct 22% (01:42) wrong based on 98 sessions
HideShow timer Statistics
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: \(\frac{1}{14} + \frac{1}{14} = \frac{1}{7}\) My approach:Probability of receiving Progaine:\(\frac{1}{14} * \frac{13}{13} = \frac{1}{14}\) Probability of receiving Ropecia, which is:(Probabilty of NOT receiving Progaine) * (Probability of receiving Ropecia among the rest): 13/14 * 1/13 = 1/14 Therefore, the answer to question is: \(\frac{1}{14} + \frac{1}{14} = \frac{1}{7}\) Is my approach correct?, Why doesn't MGMAT consider the order in the administration of the drugs? When the researcher provides Ropecia, he or she has to choose among 13 people, NOT 14. It seems they are using the P(A) + P(B)  P(A and B) formula. Please your comments.
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/myirlogbookdiary133264.html GMAT Club Premium Membership  big benefits and savings




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India

Re: A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
22 Jan 2013, 21:32
danzig wrote: Bunuel, 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! It is a very interesting point and hence I am taking it up (even though the question is directed to Bunuel). First of all, let's calculate the probability that Donald will get Ropecia. For Donald to get Ropecia, he must not get Progaine but any of the other 13 people can be administered Progaine. Probability of Donald getting Ropecia = (13/14)(1/13) = 1/14 13/14 is the probability that Donald doesn't get Progaine and 1/13 is the probability that Donald does get Ropecia. You see that the overall probability is still 1/14. Surprising, right? It is a little unintuitive. The point is that if the result of the first action is unknown, the probability of subsequent action remains the same. The probability of Donald getting Ropecia is 1/14 since there are 14 people and it stays 1/14 if we do not know who got Progaine. I have written a post detailing this effect in probability. Check it out: http://www.veritasprep.com/blog/2012/10 ... ureagain/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Math Expert
Joined: 02 Sep 2009
Posts: 58453

Re: A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
11 Feb 2012, 18:40
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? 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: \(\frac{1}{14} + \frac{1}{14} = \frac{1}{7}\) My approach:Probability of receiving Progaine: \(\frac{1}{14} * \frac{13}{13} = \frac{1}{14}\) Probability of receiving Ropecia, which is: (Probabilty of NOT receiving Progaine) * (Probability of receiving Ropecia among the rest): 13/14 * 1/13 = 1/14 Therefore, the answer to question is: \(\frac{1}{14} + \frac{1}{14} = \frac{1}{7}\) Is my approach correct?, Why doesn't MGMAT consider the order in the administration of the drugs?, when the researcher provides Ropecia, he or she has to choose among 13 people, NOT 14. It seems they are using the P(A) + P(B)  P(A and B) formula. Please your comments. This question has much simpler solution than MGMAT offered: Donald to receiver either Prograine or Ropecia must be among first two chosen patients and as there are 14 patients then the probability of this is simply 2/14=1/7.
_________________



Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1002
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs

Re: A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
11 Feb 2012, 18:44
Bunuel wrote: This question has much simpler solution than MGMAT offered: Donald to receiver either Prograine or Ropecia must be among first two chosen patients and as there are 14 patients then the probability of this is simply 2/14=1/7. Thank you Bunuel! But what do you think about my approach?, am I going in the right path? Thanks!
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/myirlogbookdiary133264.html GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 58453

Re: A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
11 Feb 2012, 19:13
metallicafan wrote: Bunuel wrote: This question has much simpler solution than MGMAT offered: Donald to receiver either Prograine or Ropecia must be among first two chosen patients and as there are 14 patients then the probability of this is simply 2/14=1/7. Thank you Bunuel! But what do you think about my approach?, am I going in the right path? Thanks! Yes, you can use P(A)+P(B)P(A and B) here: 1/14+13/14*1/130, as P(both)=0. But again this is a long way.
_________________



Intern
Joined: 25 Jul 2012
Posts: 1

Re: A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
31 Jul 2012, 09:52
Hello.. first post ever!
To dovetail off metallicafan's question, can you please explain how you know that the order does not matter? How can you make this assumption when the question specifically states, "event X, THEN event Y"
Thanks



Intern
Joined: 06 Apr 2012
Posts: 30

Re: A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
07 Dec 2012, 09:04
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? 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: \(\frac{1}{14} + \frac{1}{14} = \frac{1}{7}\) My approach:Probability of receiving Progaine:\(\frac{1}{14} * \frac{13}{13} = \frac{1}{14}\) Probability of receiving Ropecia, which is:(Probabilty of NOT receiving Progaine) * (Probability of receiving Ropecia among the rest): 13/14 * 1/13 = 1/14 Therefore, the answer to question is: \(\frac{1}{14} + \frac{1}{14} = \frac{1}{7}\) Is my approach correct?, Why doesn't MGMAT consider the order in the administration of the drugs? When the researcher provides Ropecia, he or she has to choose among 13 people, NOT 14. It seems they are using the P(A) + P(B)  P(A and B) formula. Please your comments. I am going over this question right now and I saw the solutions and I really appreciate the input guys. Bunuel my question is similar and what really throws me off is the phrase " The same logic also holds for Ropecia"  1) Do you think MGMAT just used a shortcut there to say that P(Ropecia) = 13/14 * 1/13 = 1/14 or how else do you get 1/14 for P(Ropecia)? The way I translate " The same logic also holds for Ropecia" is certainly not P(Ropecia) = 1/14 for the reason described above...please let me know if the explanation MGMAT provides sounds clear to you and perhaps what you would take out from such explanation. 2) As for your solution, if we change to the question to " what is the P(Progaine, or Ropecia, or Placebo)?" the solution would not be 3/14 or would it? P.S. Just another thought, I agree that your method is much shorter (and intuitive as well) but for those who do not have a solid grasp of seemingly more convoluted prob/comb problems such as one above (and as such, they may be viewed as those who lack "common sense" ) it is important to see all of the steps...so in this regard it is good that metallicafan clarified one way we get P(Ropecia) and fits nicely with overall thinking about probability.



Manager
Joined: 11 Aug 2012
Posts: 110

Re: A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
22 Jan 2013, 08:44
Bunuel, 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!



Intern
Joined: 07 Mar 2013
Posts: 24

Re: A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
17 Sep 2013, 03:31
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?
What should be the methodology to tackle these questions ?



Math Expert
Joined: 02 Sep 2009
Posts: 58453

Re: A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
17 Sep 2013, 03:34
vishalrastogi 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?
What should be the methodology to tackle these questions ? Merging similar topics. Please refer to the solutions above. Similar questions to practice: aboxcontains3yellowballsand5blackballsonebyone90272.htmlabagcontains3whiteballs3blackballs2redballs100023.htmleachoffourdifferentlockshasamatchingkeythekeys101553.htmlif40peoplegetthechancetopickacardfromacanister97015.htmlnewsetofmixedquestions150204100.html#p1208473abagcontains3whiteballs3blackballs2redballs100023.htmlHope this helps.
_________________



Director
Joined: 17 Dec 2012
Posts: 626
Location: India

Re: A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
17 Sep 2013, 04:25
1. The only way Donald could have got Progaine is when he is the first patient chosen. The probability of this happening is 1/14 2. The only way Donald could have got Ropecia is being the second patient chosen. For this we know he should not have been the first patient. So the probability is 1/13 * 13/14= 1/14 where 13/14 is the probability of not being chosen the first patient. 3. The probability of being given Progaine or Ropecia is the sum of the two= 1/14 + 1/14= 1/7
_________________
Srinivasan Vaidyaraman Sravna Test Prep http://www.sravnatestprep.comHolistic and Systematic Approach



Director
Joined: 17 Dec 2012
Posts: 626
Location: India

Re: A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
17 Sep 2013, 04:59
danzig wrote: Bunuel, 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! Hi, It would seem that since the second patient is chosen from only among the 13 patients, the probability of being given Ropecia is 1/13 but remember the second patient is chosen after the first patient. The actual second patient chosen could really have been the first patient chosen or he could not have been the first patient chosen. The former has a probability 1/14 and the latter 13/14. We are considering only the second case that the second patient is chosen from the remaining patients after the first patient is chosen. So instead of 1/13 * ( 1/14 + 13/14) = 1/13, we have 1/13 * (13/14)= 1/14. To elaborate, if he is chosen as the first patient he would not have been given Ropecia at all. So that affects the probability of being given Ropecia and hence would not be 1/13.
_________________
Srinivasan Vaidyaraman Sravna Test Prep http://www.sravnatestprep.comHolistic and Systematic Approach



Manager
Joined: 19 Oct 2016
Posts: 65
Location: India
Concentration: Marketing, Leadership
GMAT 1: 580 Q46 V24 GMAT 2: 540 Q39 V25 GMAT 3: 660 Q48 V34
GPA: 3.15
WE: Psychology and Counseling (Health Care)

Re: A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
09 Feb 2017, 04:24
bumpbot wrote: Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. What's up bumpbot Want to know how I solved it? Since it's an or question you addd subtract the chances of both happening... so (1/14) + (1/13)  (1/14 * 1/13) = (27/182)  (1/182)= 26/182 = 13/91 = 1/7



NonHuman User
Joined: 09 Sep 2013
Posts: 13263

Re: A medical researcher must choose one of 14 patients to
[#permalink]
Show Tags
29 Apr 2019, 08:43
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: A medical researcher must choose one of 14 patients to
[#permalink]
29 Apr 2019, 08:43






