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

Question

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

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

raj2812 · Accepted Answer

Great explanation

. 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.

Drb89 · Answer

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}

zishu912 · Answer

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

JeffTargetTestPrep · Answer

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

Kinshook · Answer

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

vrazchauhan0 · Answer

Tried solving it like this:

Given, P(A|C) = 1/2 = P(AC)/P(C)
 P(C|A) = 1/3 = P(AC)/P(A)
Find P(AC)
 
 P(C) = 2P(AC)
 P(A) = 3P(AC)

1 = P(A) + P(C) - P(AC) 
1 = 3P(AC) + 2P(AC) - P(AC) 
P(AC) = 1/4

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

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	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

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

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