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Each Employee at a certain bank is either a clerk or an agen

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Each Employee at a certain bank is either a clerk or an agen [#permalink] New post 07 May 2019, 02:14
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Question Stats:

20% (01:36) correct 80% (01:28) wrong based on 5 sessions
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) \(\frac{2}{5}\)
[Reveal] Spoiler: OA

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Re: Each Employee at a certain bank is either a clerk or an agen [#permalink] New post 08 Jun 2019, 20:54
Explanation please
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Re: Each Employee at a certain bank is either a clerk or an agen [#permalink] New post 09 Jun 2019, 02:06
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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

\(\frac{x}{c+a+x} = \frac{x}{x+2x+x} = \frac{x}{4x} = \frac{1}{4}\)

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Re: Each Employee at a certain bank is either a clerk or an agen   [#permalink] 09 Jun 2019, 02:06
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