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Question

There are 5 brilliant students in class XI and 8 brilliant students in class XII. Each class has 50 students, The odds in favour of choosing the class XI are 2:3, If the class XI is not chosen then the class XII is chosen, A student is a chosen and is found to be brilliant, find the probability that the chosen student is from class XI.

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Solution

Let E and F be the events 'Class XI is chosen' and 'Class XII is chosen' respectively,
Then P(E)=25,P(F)=35
Let A be the event 'Student chosen is brilliant'.
Then P(A/E)=550 and P(A/F)=850
P(A)=P(E).P(A/E)+P(F).P(A/F)=25.550+35.850=34250.
P(E/A)=P(E).P(A/E)P(E)P(A/E)+P(F).P(A/F)=517.

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