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Each employee at a certain bank is either a clerk or an agent or both.

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raj2812
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Each employee at a certain bank is either a clerk or an agent or both. [#permalink] New post   22 May 2018, 09:01
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Each employee at a certain bank is either a clerk or an agent or both. Of every 3 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 a bank is both an agent and a clerk?

A 1/2
B 1/3
C 1/4
D 1/5
E 2/5
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C
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raj2812
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Each employee at a certain bank is either a clerk or an agent or both. [#permalink] New post   22 May 2018, 10:21
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Dineshrambalaji wrote:
raj2812 wrote:
Each employee at a certain bank is either a clerk or an agent or both. Of every 3 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 a bank is both an agent and a clerk?

A 1/2
B 1/3
C 1/4
D 1/5
E 2/5


First equation:

two-thirds of Agents = one-half of clerk
\(\frac{1}{3} A = \frac{1}{2}C\)
\(C = \frac{2}{3} A\)


Total number of employees:
\(Total = A + C - Both\)
\(Total = A + \frac{2}{3} A - \frac{1}{3} A\)
\(Total = \frac{4}{3} A\)

\(Probability = \frac{Both}{Total}\)
\(Prob = \frac{1}{3} A / \frac{4}{3} A\)
\(Prob = \frac{1}{4}\)



Great explanation :thumbup: . However, this can be done with simple overlapping sets also..

we have 1 person who is both an agent and a clerk,
we have 2 who are only agents and 1 who is only a clerk.
So for every 4 people, there is 1 who is an agent and a clerk, and the answer is 1/4.

:-)
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Drb89
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Re: Each employee at a certain bank is either a clerk or an agent or both. [#permalink] New post   22 May 2018, 10:09
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raj2812 wrote:
Each employee at a certain bank is either a clerk or an agent or both. Of every 3 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 a bank is both an agent and a clerk?

A 1/2
B 1/3
C 1/4
D 1/5
E 2/5


First equation:

two-thirds of Agents = one-half of clerk
\(\frac{1}{3} A = \frac{1}{2}C\)
\(C = \frac{2}{3} A\)


Total number of employees:
\(Total = A + C - Both\)
\(Total = A + \frac{2}{3} A - \frac{1}{3} A\)
\(Total = \frac{4}{3} A\)

\(Probability = \frac{Both}{Total}\)
\(Prob = \frac{1}{3} A / \frac{4}{3} A\)
\(Prob = \frac{1}{4}\)
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Re: Each employee at a certain bank is either a clerk or an agent or both. [#permalink] New post   22 May 2018, 11:40
raj2812 wrote:
Each employee at a certain bank is either a clerk or an agent or both. Of every 3 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 a bank is both an agent and a clerk?

A 1/2
B 1/3
C 1/4
D 1/5
E 2/5



There is 2 overlapping set Agent and clerk
and according to the question for every 2 clerk there is also an agent and for every 3 agents there is also a clerk

so the total sample space = 4
number of employee who is both an agent and clerk = 1

so the probability of choosing an employee who is both agent and clerk = 1 /4
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Re: Each employee at a certain bank is either a clerk or an agent or both. [#permalink] New post   30 May 2018, 17:14
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raj2812 wrote:
Each employee at a certain bank is either a clerk or an agent or both. Of every 3 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 a bank is both an agent and a clerk?

A 1/2
B 1/3
C 1/4
D 1/5
E 2/5



If there are 6 agents, 2 of them are also clerks and 4 of them are agents only.

If there are 4 clerks, 2 of them are also agents and 2 of them are clerks only.

Therefore, if there are 8 employees in the bank, 4 of them are agents only, 2 of them are clerks only and 2 of them are both. Therefore, the probability that a randomly selected employee is both an agent and a clerk is 2/8 = 1/4.

Answer: C
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Each employee at a certain bank is either a clerk or an agent or both. [#permalink] New post   01 May 2022, 02:27
Given: Each employee at a certain bank is either a clerk or an agent or both. Of every 3 agents one is also a clerk. Of every two clerks, one is also an agent.

Asked: What is the probability that an employee randomly selected from a bank is both an agent and a clerk?


Clerk~ClerkTotal
Agentx/32x/3x
~Agentx/301-x=x/3; x=3/4
Total2x/32x/31=4x/3; x=3/4



Clerk~ClerkTotal
Agentx/3=1/42x/3=1/2x=3/4
~Agentx/3= 1/401-x=x/3 = 1/4
Total2x/3=1/22x/3=1/21=4x/3


Probability that that an employee randomly selected from a bank is both an agent and a clerk = 1/4

IMO C
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Re: Each employee at a certain bank is either a clerk or an agent or both. [#permalink] New post   25 Jun 2023, 14:30
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Re: Each employee at a certain bank is either a clerk or an agent or both. [#permalink]
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