Question

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 1

Let A = Employees are graduates

B = Employees are non-graduates

and E = Working in administrative positions

Given P(A) = `15/100`,

P(B) = `85/100`

`P(E/A) = 80/100`, 

`P(E/B) = 10/100`

By Bayes' theorem,

`P(A/E) = (P(A)*P(E/A))/(P(A)*P(E/A) + P(B)*P(E/B))`

`P(A/E) = (15/100 xx 80/100)/(15/100 xx 80/100 + 85/100 xx 10/100)`

= `(15 xx 80)/(15 xx 80 + 85 xx 10)`

= `1200/(1200 + 850)`

= `1200/2050`

= `120/205`

= `24/41`