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 1

Step-by-step explanation:

Given 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?

• Let A be person has heart attack
• Let B be person treated with medicine and yoga
• Let C be person treated with drug
• So P(A) = 40% = 0.40
• Also meditation and yoga and drug has equal probabilities P(B) = 1/2 and P(C) = 1/2
• We need to find if the person selected has a heart attack and the probability that the person followed meditation and yoga  
• So meditation reduces the risk by 30% and so there is a risk of 70% = 0.70
• P(A/ B) = P(heart attack) x risk
•       = 0.40 x 0.70
•   = 0.28
• The drug reduces the risk by 25% so there is a risk of 75% = 0.75
• So P(A/C) = P(heart attack) x risk
•                = 0.40 x 0.75
•                    = 0.30
• Therefore P(B/A) = P(B) P(A/B) / P(A). P(A//B) + P(C).P(P/C)
•                = ½ x  0.28 / ½ x 0.28 + ½ x 0.30
•         = 0.28 / 0.28 + 0.30
•             = 0.28 / 0.58
•   = 14 / 29

Reference link will be

https://brainly.in/question/983982