Bayes' Theorem Problem from ISC 2023 Maths Paper

In a company, 15% of the employees are graduates and 85% of the employees are non-graduates. as per the annual report of the company, 80% of the graduate employees and 10% of the non-graduate employees are in the administrative positions. find the probability that an employee selected at random from those working in administrative positions will be a graduate. 

Answer:

Step-by-step explanation:

Let G be the event that the selected employee is a graduate, and NG be the event that the selected employee is non-graduate.

Clearly, G and NG forms a mutually exclusive and exhaustive set of events.

Further, let A be the event that the selected employee works in administrative office.

According to the problem, we have to find, the selected employee is a graduate given he/she works in the administrative position P(G/A).

By Bayes' theorem,

Now, Probability of an employee to be graduate =

Probability of an employee to be non-graduate =

Probability of an employee working in administrative office given he is a graduate =

( as 80% of the graduate employee works in the administrative positions)

Probability of an employee working in administrative office given he is a non-graduate =

( as 10% of the non-graduate employee works in the administrative positions)

Substituting the values in

, we get,