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

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Re: Each employee at a certain bank is either a clerk or an agent or both. [#permalink]
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]
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.

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Each employee at a certain bank is either a clerk or an agent or both. [#permalink]
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 ~Clerk Total Agent x/3 2x/3 x ~Agent x/3 0 1-x=x/3; x=3/4 Total 2x/3 2x/3 1=4x/3; x=3/4

 Clerk ~Clerk Total Agent x/3=1/4 2x/3=1/2 x=3/4 ~Agent x/3= 1/4 0 1-x=x/3 = 1/4 Total 2x/3=1/2 2x/3=1/2 1=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]
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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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