An immigration law firm assists individuals from around the world in pursuing te

Question

An immigration law firm assists individuals from around the world in pursuing temporary and permanent visas for living and/or working in the United States. Presently, the attorney processes 20% of the visa applications, while the senior paralegal processes the remaining 80% of the visa applications. Letting A stand for attorney and S stand for senior paralegal, any randomly chosen visa application has a 20% chance of being processed by A and an 80% by S. When a visa application is processed, the processor can make an error. The attorney makes an error on 1 in every 25 applications. On the other hand, the senior paralegal makes an error on 1 in every 10 applications.

• What is the probability that a visa application was processed by the senior paralegal and was processed correctly?

• What is the probability that a visa application was processed by the attorney if we know it was processed correctly?

Explanation / Answer

Event A: Attorney processes the visa, P(A) = 0.20
Event S: Senior paralegal processes the visa, P(S) = 0.80
Event E: Making an error in visa application process
P(E | A) = 1/25 = 0.04
P(E | S) = 1/10 = 0.1
Event Ec : Visa application was processed correctly
a.
P(S Ec) = P(S) . P(Ec | S) = P(S) . [1 - P(E | S)] = 0.80 x (1 - 0.1) = 0.72

b.
P(A | Ec) = P(A Ec) / P(Ec)
Using total law of probability, we first find P(E)
P(E) = P(S) P(E | S) + P(A) P(E | A) = (0.80 x 0.1) + (0.20 x 0.04) = 0.088
P(Ec) = 1 - P(E) = 0.912
P(A Ec) = P(A) P(Ec | A) = 0.20 x (1 - 0.04) = 0.192
P(A | Ec) = 0.192/0.912 = 0.2105

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