Question:
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?
Answer:
Let A denote the events that a person has a heart attack
E1 denotes the selected person followed the course of yoga and meditation
E2 denotes the person adopted the drug prescription
Now according to question
P(A) = 40% = 40/100 = 0.4
P(E1 ) = P(E2 ) = 1/2
Now
P(A/E1 ) = 0.4 * 0.7 = 0.28
P(A/E2 ) = 0.4 * 0.75 = 0.30
Probability that the patient suffering a heart attack followed a course of meditation and yoga is P(E1 /A)
=> P(E1 /A) = {P(E1 ) *P(A/E1 )}/{P(E1 )*P(A/E1 ) + P(E2 )*P(A/E2 )}
= (1/2 * 0.28)/{1/2 * 0.28 + 1/2 * 0.30}
= 0.14/(0.14 + 0.15)
= 0.14/0.29
= 14/29
So probability that the patient suffering a heart attack followed a course of meditation and yoga is 14/29.
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