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probability question

Expert replies
by sana.noor » Mon Mar 04, 2013 10:22 am
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)1/2
b)1/3
c)1/4
d)1/5
e)2/5

C

Source: Nova Math
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Source: — Problem Solving |

by hemant_rajput » Mon Mar 04, 2013 10:35 am
Of every three agents, one is also a clerk. Let A, B and C are agents and one of them is clerk too, say B.

Of every two clerks, one is also an agent. Let B and D are clerks. Now we know that B is agent too, Now B and D are in accordance with the mentioned statement.

total outcome = 4 [A,B,C,D]
Favorable outcome = 1, i.e. B

1/4

Answer is C
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by Anurag@Gurome » Mon Mar 04, 2013 9:27 pm
sana.noor wrote: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?
For each person who is both agent and clerk, we have two agents and one clerk.
Hence, among (1 + 2 + 1) = 4 people there is only one person who is both agent and clerk.

Required probability = 1/4

The correct answer is C.
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