 Hi and welcome to the session. I am Deepika here. Let's discuss a question which says In answering a question on a multiple-choice test a student either knows the answer or guesses. Let 3 over 4 be the probability that he knows the answer and 1 over 4 be the probability that he guesses Assuming that a student who guesses at the answer Will be correct with probability 1 over 4. What is the probability that the student knows the answer Given that he answered it correctly So let's start the solution now according to the question a student either knows the answer or guesses Let 3 by 4 be the probability that he knows the answer and 1 over 4 be the probability that he guesses the answer so let even be the event that The student knows answer to be the event that he guesses the answer then probability of even is equal to 3 over 4 and probability of e2 is equal to 1 over 4 again Let a be the event of getting a correct answer now probability of the event a Given even has occurred that is probability that the student giving correct answer knows it is equal to 1 Because when the student knows the answer he will always give the correct answer Again according to the question a Student who guesses at the answer will be correct with probability 1 over 4 so probability of The event a given e2 has occurred that is probability that the student giving Correct answer guesses answer is equal to 1 over 4 now we have to find The probability that the student knows the answer given that he answered it correctly is given by probability of even upon a therefore By Bayes theorem. We have probability of even Upon a is equal to probability of even Into probability of a upon even over probability of even into probability of a upon even plus probability of e2 into probability of a upon e2 Now we have probability of even is 3 upon 4 and probability of e2 is 1 upon 4 and probability of a upon even is 1 and probability of a upon e2 is 1 over 4 So on substituting these values we have probability of even upon a is equal to 3 upon 4 Into 1 over 3 upon 4 into 1 Plus 1 upon 4 into 1 upon 4 and this is equal to 3 over 4 upon 12 Plus 1 over 16 and this is again equal to 3 over 4 into 16 over 13 and This is again equal to 12 over 13 Hence the probability that the student knows the answer given that he answered it correctly is 12 over 13 So this is the answer for the above question This completes our session. I hope you have enjoyed the session. Bye and have a nice day