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 ean chouse any one of the two uplions with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. The probability that the patient followed a course of meditation and yoga is

• A. $\frac{1}{29}$
• B. $\frac{28}{29}$
• C. $\frac{15}{29}$
• D. $\frac{14}{29}$

Answer 1

Answer: (D)

Let $A,E_1$, and $E_2$, 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,
$P(A)=0.40;P\left(E_1\right)=P\left(E_2\right)=\frac{1}{2}$
$P\left(A|E_1\right)=0.40\times 0.70=0.28;P\left(A|E_2\right)=0.40\times 0.75=0.30$
Probability that the patient suffering a heart attack followed course of meditation and yoga is given by $P\left(E_1|A\right)$.
$P\left(E_1|A\right)=\frac{P\left(E_1\right)P\left(A|E_1\right)}{P\left(E_1\right)P\left(A|E_1\right)+P\left(E_2\right)P\left(A|E_2\right)}$
$=\frac{\frac{1}{2}\times 0.28}{\frac{1}{2}\times 0.28+\frac{1}{2}\times 0.30}=\frac{14}{29}$