Question

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let `3/4`be the probability that he knows the answer and `1/4`be the probability that he guesses. Assuming that a student who guesses at the answer with probability 1/4. what is the probability that the student knows the answer given that he answers correctly.? Select the correct answer from above options

Answer 1

Probablity student knows the answer, P(A)=34 Probablity student knows the answer, P(B)=14 Probablity of correct answer when student knows the answer, P(CA)=1 Probablity of correct answer when student guesses the answer, P(CB)=14 So, probablity student gives answer correctly, when he knows the answer, P(AC)=P(A)⋅P(CA)P(A)⋅P(CA)+(P(B)⋅P(CB)) =34⋅1(34)+(14)(14)=341316=1213