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
My take : Suppose the 12 ppl are A B C D E F G H I J K L
Then according to the problem - one out of every 3 agents are clerks so , C F I L are both clerks and agents . And one out of every 2 clerks are agents , so B D F H J L are both clerks and agents .Combining both F and L are both clerks and agents . So the probability should be 2/12 = 1/6. Where am i going wrong ?
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
My take : Suppose the 12 ppl are A B C D E F G H I J K L
Then according to the problem - one out of every 3 agents are clerks so , C F I L are both clerks and agents . And one out of every 2 clerks are agents , so B D F H J L are both clerks and agents .Combining both F and L are both clerks and agents . So the probability should be 2/12 = 1/6. Where am i going wrong ?
