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Question
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 and yoga. Interpret the result and state which of the above stated methods is more beneficial for the patient.
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.
`therefore P(A)=0.40`
`P(E_1)=P(E_2)=1/2`
`P(A|E_1)=0.40xx0.70=0.28P(A|E_2)=0.40xx0.75=0.30`
Probability that the patient suffering a heart attack followed a course of meditation and yoga is given by `P (E1|A).`
`P(E_1|A)=(P(E_1)P(A|E_1))/(P(E_1)P(A|E_1)+P(E_2)P(A|E_2))`
`=(1/2xx0.28)/(1/2xx0.28+1/2xx0.30)`
`=14/29`
Let us calculate `P(E_2|A)`
`P(E_2|A)=(P(E_2)P(A|E_2))/(P(E_1)P(A|E_1)+P(E_2)P(A|E_2))`
`=(1/2xx0.30)/(1/2xx0.28+1/2xx0.30)`
`=15/29`
Since `P(E_1|A)< P(E_2|A) ` the course of yoga and meditation is more beneficial for a person having chances of heart attack.
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