Question
Assume that the chances of a patient having a heart attack are 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of a certain drug reduces its chance 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?
Solution
Let E1 and E2 be the events
E1 : Treatment of yoga and meditation
E2 : Treatment of prescription of certain drugs
Let A denotes that a person has heart attack
∴ P(A) = 40% = 0.40
Yoga and mediation reduces the heart risk by 30%
i.e. inspite of getting yoga and meditation treatment heart risk is 70% of the 0.40
∴ P(A | E1) = 0.40 × 0.70 = 0.28
Drug prescription reduces the heart risk by 25%.
Even after adopting the drug prescription heart risk is 75% of the 0.40
∴ P(A | E2) = 0.40 × 0.75 = 0.30
