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प्रश्न
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.
उत्तर
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`
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