CBSE Class 12 Math 2013 Solved Paper

Question : 29

Total: 29

Assume that the chances of a patient having a heart attack is 40%. Assuming that a meditation and yoga course reduces the risk of heart attack by 30% and prescription of 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

Solution:

Let A, E1, and E2, respectively denote the events that a person has a heart attack, the selected person followed the course of yoga and meditation, and the person adopted the drug prescription.
∴ P (A) = 0.40
P (E1) = P (E2) =

P (A|E1) = 0.40 × 0.70 = 0.28
P (A|E2) = 0.40 × 0.75 = 0.30
Probability that the patient suffering a heart attack followed a course of meditation and yoga = P (E1|A)
=

P(E1)P(A|E1)

P(E1)P(A|E1)+P(E2)P(A|E2)

×0.28

×0.28+

×0.30

28+30

Now, calculate P (E2|A)
P (E2|A) =

P(E2)P(A|E2)

P(E1)P(A|E1)+P(E2)P(A|E2)

×0.30

×0.28+

×0.30

28+30

Since P (E1|A) < P (E2|A), the course of yoga and meditation is more beneficial for a patient.

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