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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.
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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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