(Solved) A college biology class consists of 8% freshmen, 27% sophomores, 45 % juniors and 20% seniors. During an exam, 22% of the freshmen, 17% of the sophomores, 12 % of the juniors, and 5% of the seniors wrote their answers in pen. If you would select an exam at random and find that the answers were written in pen, what is the probability that the exam was written by a freshmen?

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 Question :

A college biology class consists of 8% freshmen, 27% sophomores, 45 % juniors and 20% seniors. During an exam, 22% of the freshmen, 17% of the sophomores, 12 % of the juniors, and 5% of the seniors wrote their answers in pen. If you would select an exam at random and find that the answers were written in pen, what is the probability that the exam was written by a freshmen?


Explanation :

Let us consider following events. 

E1 = A college biology class consists of freshmen

E2 = A college biology class consists of sophomores

E3 = A college biology class consists of juniors

E4 = A college biology class consists of seniors

And P = student wrote their answers in pen 

If answers were written in pen, probability that the exam was written by a freshmen P(E1 | P) = 0.1380


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