In answering a question on a multiple choice test,a student either knows the answer or guesses .Let 3/4 be the probabillity that he knows the answer and 1/4 be the probability that he guesses.Assuming that a student who guesses at the answer will be correct with probability 1/4.what is the probability that the student knows the answer given that he answered it correctly?

Asked by DIPTI PRIYA | 16th Mar, 2011, 12:00: AM

Expert Answer:

Dear Student,
Here is the solution:
let E be the event where the student gets the answer right, this can be the result of 2 separate events
E1- he knows the answers hence marks it correct
E2- he guesses and gets it correct

if E1 happens then the prob that he gets it correct P(E|E1)= 1
given P(E1)= 3/4

if E2 happens then the prob that he gets it correct P(E|E2)= 1\4
given P(E2)= 1\4

using baye's theorem
P(E1|E)= P(E|E1) x P(E1)/( P(E1) P(E|E1) +P(E2)P(E|E2) )
=(1 x 3/4)/( 3/4 x 1 + 1/4 x 1/4)
=12/13
Hope this helps!

Regards
Team Topperlearning.

Answered by  | 16th Mar, 2011, 07:37: AM

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