 Hello, I am welcome to the session. I am Deepika here. Let's discuss a question which says Assume that the chances of a patient having a heart attack is 40% it is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25% At a time a patient can choose any one of the two Options with equal probabilities. It is given that after going through one of the two options the patient Selected at random suffers a heart attack. Find the probability that the patient followed a course of Meditation and yoga So let's start the solution now according to the given question the chances of a patient having a heart attack is 40% and Meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25% So a patient has two options to reduce the risk of heart attack either by Meditation and yoga course or by prescription of a certain drug let even be the event of choosing a meditation and yoga course to be the event of choosing prescription of a certain drug therefore Probability of even is equal to probability of e2 and This is equal to 1 over 2 Now the chances of a patient having a heart tag is 40% Let a be the event a patient have a heart attack therefore probability of a Which is given to us is 40% and this is equal to 0.4 0 now Meditation and yoga course reduce the risk of heart attack by 30% So in spite of getting meditation and yoga course chances of a patient having a heart attack is 70% of 40% so probability of heart risk in spite of choosing meditation and yoga course that is probability of a upon even and This is equal to 70% of 0.40 and This is again equal to 0.70 into 0.40 and this is equal to 0.28 Again, we are given prescription of certain drug reduces the risk of heart attack by 25% so probability of heart risk in spite of choosing prescription of a certain drug that is probability of a upon e2 and This is equal to 75% of 0.40 and This is again equal to 0.75 into 0.40 which is equal to 0.30 Now according to the question it is given that after going through one of the two options The patient selected at random suffers a heart attack find the probability that the patient followed a course of meditation and yoga so The probability that the patient who followed meditation and yoga course a heart attack this is given by probability of Even upon a hence by using Bayes theorem probability of Upon a is equal to probability of e i into probability of a upon e i over Sigma probability of e j Into probability of a upon e j j varying from 1 to n therefore Probability of even upon a is equal to probability of e 1 into probability of a upon e 1 over probability of e 1 into probability of a upon e 1 plus probability of e 2 Into probability of a upon e 2 now we have probability of even is equal to probability of e 2 is equal to 1 over 2 and probability of a upon e 1 is 0.2 a and probability of a upon e 2 is 0.30 So on substituting these values, we have probability of even upon a is equal to 1 over 2 into 0.2 a over 1 over 2 Into 0.2 a Plus 1 over 2 into 0.3 0 and this is equal to 0.2 a Over 0.2 a plus 0.3 0 Here we have cancelled 1 over 2 in the numerator and the denominator And this is equal to 0.2 a over 0.5 a and This is again equal to 0.2 a over 0.5 a which is equal to 14 over 29 so the Probability that the patient who followed a course of meditation and yoga Have a heart attack is 14 over 29 So this is the answer for the question this completes our session I hope the solution is clear to you. Bye and have a nice day