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Updated on: 13 Aug 2018, 00:02
Originally posted by EgmatQuantExpert on 06 Jul 2018, 04:00.
Last edited by EgmatQuantExpert on 13 Aug 2018, 00:02, edited 2 times in total.
Last edited by EgmatQuantExpert on 13 Aug 2018, 00:02, edited 2 times in total.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
39% (03:01) correct
61%
(03:07)
wrong
based on 226
sessions
History
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Not Attempted Yet
e-GMAT Question of the Week #6
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 \(\frac{3}{5}\) 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?
To access all the questions: Question of the Week: Consolidated List
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 \(\frac{3}{5}\) 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
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
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
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
General Discussion
Updated on: 13 Aug 2018, 00:35
Originally posted by EgmatQuantExpert on 09 Jul 2018, 06:44.
Last edited by EgmatQuantExpert on 13 Aug 2018, 00:35, edited 1 time in total.
Last edited by EgmatQuantExpert on 13 Aug 2018, 00:35, edited 1 time in total.
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Hey everyone,
We will post the solution very soon. Till then, try it one more time and post your analysis.
We will post the solution very soon. Till then, try it one more time and post your analysis.
