


Bayes theorem
Ex 13.3, 2 Important
Ex 13.3, 3
Misc 3
Ex 13.3, 4 Important
Ex 13.3, 9
Ex 13.3, 5
Ex 13.3, 13 (MCQ) Important
Example 21 Important
Ex 13.3, 6 Important
Ex 13.3, 10 Important
Example 18 Important
Example 17 Important
Ex 13.3, 7
Ex 13.3, 8 Important
Example 19 Important
Ex 13.3, 11
Ex 13.3, 12 Important
Example 37 Important
Example 20 Important
Example 33 Important
Misc 12
Misc 16 Important
Misc 13 Important You are here
Bayes theorem
Misc 13 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?Normal risk of heart attack is 40%. If we do meditation and yoga, it reduces risk by 30% i.e. risk becomes 40% Γ 70% = 28% Let A : Person has heart attack E1 : Person is treated with meditation & yoga E2 : Person is treated with drug Given, P(A) = 40 % = 0.40 Also, given that meditation & yoga and drug has equal probabilities P(E1) = 1/2 , P(E2) = 1/2 We have to find that if a person selected has an heart attack, what is the probability that the person followed meditation & yoga. i.e. P(E1|A) P(E1|A) = (π(πΈ_1 ).π(π΄|πΈ_1))/(π(πΈ_1 ).π(π΄|πΈ_1)+π(πΈ_2 ).π(π΄|πΈ_2) ) P(A|E1) i.e. Probability of having heart attack if he is treated with meditation Meditation reduce the risk by 30% , so there is a risk of 70% i.e 0.70 P(A|E1) = P(heart attack) Γ Risk = 0.40 Γ 0.70 = 0.28 P(A|E2) i.e. Probability of having heart attack if he is treated with drugs The daring reduce the risk by 25% , so there is a risk of 75% i.e. 0.75 P(A|E2) = P(heart attack) Γ Risk = 0.40 Γ 0.75 = 0.30 Therefore, P(E1|A) = (π(πΈ_1 ).π(π΄|πΈ_1))/(π(πΈ_1 ).π(π΄|πΈ_1)+π(πΈ_2 ).π(π΄|πΈ_2) ) = (1/2 Γ 0.28)/(1/2 Γ 0.28 + 1/2 Γ 0.30) = 0.28/(0.28 + 0.30) = 0.28/0.58 = 14/29