Question

Assume that the chances of a patient having a heart attack are $40\%$. It is also assumed that a meditation and yoga course reduce the risk of heart attack by $30\%$ and the prescription of certain drugs reduces its chances by $25\%$. At a time a patient can choose any 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

Probability of patient having heart attack $=0.4$

Probability that patient won't have heart attack $=0.6$

Let $E_1$ be the event of the patient following a course of meditation and yoga.

Let $E_2$ be the event of the patient following a course of prescription of drugs.

$\Rightarrow P\left(\frac{A}{E_1}\right)=P\left(\frac{A}{E_2}\right)=0.4$

$\Rightarrow P\left(E_1\right)=0.3$ $P\left(E_2\right)=0.25$

$\therefore P\left(\frac{E}{E_1}\right)=\frac{P\left(E_1\right)P\left(\frac{A}{E_1}\right)}{P\left(E_1\right)P\left(\frac{A}{E_1}\right)+P\left(E_2\right)P\left(\frac{A}{E_1}\right)}$

$=\frac{0.3\times 0.4}{0.3\times 0.4+0.25\times 0.4}$

$=0.55$

Hence, the answer is $\mathrm{0.55.}$