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Each Employee at a certain bank is either a clerk or an agen
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07 May 2019, 02:14
07 May 2019, 02:14
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Question Stats:
41% (02:04) correct
58% (01:59) wrong based on 39 sessions
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Each Employee at a certain bank is either a clerk or an agent or both. Of every three agents, one is also a clerk. Of every two clerks, one is also an agent. What is the probability that an employee randomly selected from the bank is both an agent and a clerk?
(A) \(\frac{1}{2}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{1}{4}\)
(D) \(\frac{1}{5}\)
(E) \(\frac{2}{5}\)
(A) \(\frac{1}{2}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{1}{4}\)
(D) \(\frac{1}{5}\)
(E) \(\frac{2}{5}\)
Re: Each Employee at a certain bank is either a clerk or an agen
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08 Jun 2019, 20:54
08 Jun 2019, 20:54
Explanation please
Re: Each Employee at a certain bank is either a clerk or an agen
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09 Jun 2019, 02:06
09 Jun 2019, 02:06
Expert Reply
This is tough. Is a mix of overlapping set and probability. However, once you have found the OS the rest is easy.
In my opinion, attacking the question using number is cumbersome.
Now, c stands for Clerks. a stands for Agents and x stands for both.
Total Clerks: c+x
Total Agents: a+x
Total: c+a+x
Divide in small chunks the question.
Of every three agents, one is also a clerk.
means that an x employee which is part of both is over the agents category only \(\frac{x}{a+x}= \frac{1}{3}\) ; a = 2x
Of every two clerks, one is also an agent.
\(\frac{x}{c+x} = \frac{1}{2}\) ; c=x
The probability is
\(\frac{x}{c+a+x} = \frac{x}{x+2x+x} = \frac{x}{4x} = \frac{1}{4}\)
Hope this helps
In my opinion, attacking the question using number is cumbersome.
Now, c stands for Clerks. a stands for Agents and x stands for both.
Total Clerks: c+x
Total Agents: a+x
Total: c+a+x
Divide in small chunks the question.
Of every three agents, one is also a clerk.
means that an x employee which is part of both is over the agents category only \(\frac{x}{a+x}= \frac{1}{3}\) ; a = 2x
Of every two clerks, one is also an agent.
\(\frac{x}{c+x} = \frac{1}{2}\) ; c=x
The probability is
\(\frac{x}{c+a+x} = \frac{x}{x+2x+x} = \frac{x}{4x} = \frac{1}{4}\)
Hope this helps
