Author 
Message 
TAGS:

Hide Tags

eGMAT Representative
Joined: 04 Jan 2015
Posts: 2014

P, Q, and R each try to execute a job and create a report on it. The
[#permalink]
Show Tags
Updated on: 13 Aug 2018, 00:02
Question Stats:
34% (02:59) correct 66% (02:14) wrong based on 128 sessions
HideShow timer Statistics
eGMAT Question of the Week #6P, Q, and R each try to execute a job and create a report on it. The individual probabilities for their completion of the jobs are \(\frac{1}{3}\), \(\frac{2}{3}\), and \(\frac{3}{5}\) and the probability for any of them not to finish the report is \(\frac{2}{5}\). If one can write the report only after finishing the job, then what is the probability that only P and Q will complete their jobs and finish their reports? A. \(\frac{4}{625}\)
B. \(\frac{4}{125}\)
C. \(\frac{32}{625}\)
D. \(\frac{4}{25}\)
E. \(\frac{32}{125}\) To access all the questions: Question of the Week: Consolidated List
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



RC Moderator
Status: Perfecting myself for GMAT
Joined: 22 May 2017
Posts: 637
Concentration: Nonprofit
GPA: 4
WE: Engineering (Computer Software)

Re: P, Q, and R each try to execute a job and create a report on it. The
[#permalink]
Show Tags
Updated on: 09 Jul 2018, 20:39
P, Q, and R each try to execute a job and create a report on it. Completing the job and finishing the report by P, Q and R are independent of each other. GIven probability for any of them not finishing the report is \(\frac{2}{5}\) probability for any of them finishing the report is \(1\frac{2}{5} = \frac{3}{5}\) To find out the probability that only P and Q will complete their jobs and finish their reports We need to find Required probability is the product of three of the following probabilitites P(P will complete his job AND finish the report) P(Q will complete his job AND finish the report) P(R will not complete his job) OR P(R will complete his job AND not finish the report) probability that P will complete his job and finish the report = \(\frac{1}{3} * \frac{3}{5} = \frac{1}{5}\) probability that Q will complete his job and finish the report =\(\frac{2}{3} * \frac{3}{5} = \frac{2}{5}\) probability that R will not complete his job = \(1  \frac{3}{5} = \frac{2}{5}\) probability that R will complete his job and not finish the report = \(\frac{3}{5} * \frac{2}{5} = \frac{6}{25}\) Substituting the above values, we get \((\frac{1}{5})(\frac{2}{5})(\frac{2}{5} + \frac{6}{25}) = \frac{32}{625}\) Hence option C
_________________
If you like my post press kudos +1
New  RC Butler  2 RC's everyday
Tag me in RC questions if you need help. Please provide your analysis of the question in the post along with the tag.
Originally posted by workout on 06 Jul 2018, 21:40.
Last edited by workout on 09 Jul 2018, 20:39, edited 1 time in total.



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2014

P, Q, and R each try to execute a job and create a report on it. The
[#permalink]
Show Tags
Updated on: 13 Aug 2018, 00:35



Intern
Status: Prep Mode
Joined: 16 Jan 2015
Posts: 17
Location: India
WE: Programming (Computer Software)

Re: P, Q, and R each try to execute a job and create a report on it. The
[#permalink]
Show Tags
Updated on: 09 Jul 2018, 11:55
Given that:
Probability that \(P\) execute the job = \(\frac{1}{3}\) Probability that \(Q\) execute the job = \(\frac{2}{3}\) Probability that \(R\) execute the job = \(\frac{3}{5}\)
Probability that anyone not finishing the report = \(\frac{2}{5}\) => Probability that anyone finish the report = 1  \(\frac{2}{5}\) = \(\frac{3}{5}\)
Given that only \(P\) and \(Q\) will execute the job and finish the report. So,\(R\) will not execute the job
Therefore Probability of \(R\) not executing the job = 1 \(\frac{3}{5}\) = \(\frac{2}{5}\)
Required probability = (P execute the job and finish report) x ( Q execute the job and finish the report) x (R not executing the job) = \((\frac{1}{3} * \frac{3}{5}) ( \frac{2}{3} * \frac{3}{5}) (\frac{2}{5})\) = \(\frac{1}{5} * \frac{2}{5} * \frac{2}{5}\) = \(\frac{4}{125}\) Answer = B



Intern
Joined: 19 Nov 2017
Posts: 15

Re: P, Q, and R each try to execute a job and create a report on it. The
[#permalink]
Show Tags
09 Jul 2018, 10:12
I did go with C but the OA says B. So here is why it could be B.
P(E) for P and Q to complete their jobs and reports = [(P(A)*P(B)*P(C) all completing the Job) * (P(A)*P(B) completing the Report *P(C) not completing the Report)] + [(P(A)*P(B) completing the Job * P(C) not completing the Job ) * (P(A)*P(B) completing the Report *P(C) not completing the Report)].
We should remember that when C does not complete this job it also implies that he cannot complete his report.
Substituting the values we get >[\((1/3*2/3*3/5)* (3/5*3/5*2/5) = 12/625\)] + [\((1/3*2/3*2/5)* (3/5*3/5*2/5) = 8/625\)] = \(20/625\) = \(4/125\)
Do let me know if my understanding is wrong.
Aditya. Do give kudos if you find this answer helpful.



Manager
Joined: 06 May 2018
Posts: 59

Re: P, Q, and R each try to execute a job and create a report on it. The
[#permalink]
Show Tags
09 Jul 2018, 11:42
The reason why I calculated B and not C is the last part of the question: then what is the probability that only P and Q will complete their jobs and finish their report For me completing the job and finishing their report implies that R was not able to complete the job. Therefore, it is not necessary to take into account, that R could have completed the job but not the report.



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2014

P, Q, and R each try to execute a job and create a report on it. The
[#permalink]
Show Tags
Updated on: 13 Aug 2018, 00:33
Solution Given:• P, Q, and R each try to execute a job and create a report on it • The individual probabilities for their completion of the jobs are \(\frac{1}{3}\), \(\frac{2}{3}\), and \(\frac{3}{5}\) • The probability for any of them not to finish the report is \(\frac{2}{5}\)
o Hence, the probability of finishing the report = \((1 – \frac{2}{5}) = \frac{3}{5}\) • One can write the report only after finishing the job To find:• The probability that only P and Q will complete their jobs and finish their reports Approach and Working: it is given that, as per the favourable event, only P and Q will complete their jobs and finish their reports • The probability that P will execute the job and finish the report = \(\frac{1}{3} * \frac{3}{5} = \frac{1}{5}\) • The probability that Q will execute the job and finish the report = \(\frac{2}{3} * \frac{3}{5} = \frac{2}{5}\) Now, as only P and Q will complete their jobs and finish their reports, it also means, there are two possibilities exist for R • Either R will not finish the job, and definitely not finish the report (as one cannot finish the report without executing the job)
o Probability of this event = \((1 – \frac{3}{5}) * \frac{2}{5} = \frac{2}{5} * \frac{2}{5} = \frac{4}{25}\) • Or else, R will execute the job but will not finish the report
o Probability of this event = \(\frac{3}{5} * \frac{2}{5} = \frac{6}{25}\) So, we can say, • Probability (only P and Q will complete their jobs and finish their reports) = P (P completes job & finish report) AND P (Q completes job & finish report) AND [P (R does not complete the job & does not complete the report) OR P (R does complete the job & does not complete the report) = \(\frac{1}{5} * \frac{2}{5} * [\frac{4}{25} + \frac{6}{25}]\) = \(\frac{1}{5} * \frac{2}{5} * \frac{2}{5}\) = \(\frac{4}{125}\) Hence, the correct answer is option B. Answer: B
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Intern
Joined: 25 Nov 2017
Posts: 28
Location: India
GMAT 1: 590 Q47 V25 GMAT 2: 700 Q50 V34
GPA: 3.56

Re: P, Q, and R each try to execute a job and create a report on it. The
[#permalink]
Show Tags
21 Jul 2018, 10:56
Hi expert,
I can not understand why we need to consider the probability of R as the question asks to find the probability that only P and Q will complete their jobs and finish their reports.
Plz help.



Intern
Joined: 19 May 2018
Posts: 15

Re: P, Q, and R each try to execute a job and create a report on it. The
[#permalink]
Show Tags
21 Jul 2018, 15:18
Hello expert, request you explain this how do we consider the probability Sent from my CPH1727 using GMAT Club Forum mobile app



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2014

Re: P, Q, and R each try to execute a job and create a report on it. The
[#permalink]
Show Tags
22 Jul 2018, 06:38
BARUAH wrote: Hi expert,
I can not understand why we need to consider the probability of R as the question asks to find the probability that only P and Q will complete their jobs and finish their reports.
Plz help. Hey BARUAH, If you read the question carefully, the favourable event is defined as " only P and Q will complete their jobs and finish their reports." It means we have to ensure that R cannot complete the job and finish the report. For this reason we have to consider the probability of R. Hope this answers your query.
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2014

Re: P, Q, and R each try to execute a job and create a report on it. The
[#permalink]
Show Tags
22 Jul 2018, 06:40



Intern
Joined: 15 Jul 2018
Posts: 6

Re: P, Q, and R each try to execute a job and create a report on it. The
[#permalink]
Show Tags
26 Jul 2018, 22:09
Hello EgmatQuantExpert, thank you for the detailed explanation. My mistake was to miss the probability of not finishing the report when R did not even finish his job. I thought that since we are told that one cannot even start his report if he didn't finish his job, hence there is no need to multiply 2/5 (13/5  probability that R will not finish his job) with 2/5 (probability of not finishing a report). Please help me understand why we need to take into consideration the probability of not finishing a report when we know that R did jot finish his job, hence he cannot even start his report? Thanks a lot!




Re: P, Q, and R each try to execute a job and create a report on it. The &nbs
[#permalink]
26 Jul 2018, 22:09






