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 changes 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. Then, the probability that the patient followed a course of meditation and yoga, is

• A. $\frac{11}{29}$
• B. $\frac{2}{29}$
• C. $\frac{14}{29}$
• D. $\frac{1}{29}$

Answer 1

Answer: (C)

Let $E_1$ : the event that the patient follows meditation and yoga and
$E_2$ : the event that the patient uses drug.
$\therefore E_1$ and $E_2$ are mutually exclusive events and
$P\left(E_1\right)=P\left(E_2\right)=\frac{1}{2}$
Let $E$ : the event that the selected patient suffers a heart attack
$\therefore P\left(\frac{E}{E_1}\right)=\frac{40}{100}\left(1-\frac{30}{100}\right)=\frac{28}{100}$
$P\left(\frac{E}{E_2}\right)=\frac{40}{100}\left(1-\frac{25}{100}\right)=\frac{30}{100}$
$\therefore P$ (patient who suffers heart attack follows meditation and yoga)
$=P\left(\frac{E_1}{E}\right)=\frac{P\left(\frac{E}{E_1}\right)P\left(E_1\right)}{P\left(\frac{E}{E_1}\right)P\left(E_1\right)+P\left(\frac{E}{E_2}\right)P\left(E_2\right)}$
$=\frac{\frac{28}{100}\times \frac{1}{2}}{\frac{28}{100}\times \frac{1}{2}+\frac{30}{100}\times \frac{1}{2}}$
$=\frac{\frac{14}{100}}{\frac{14}{100}+\frac{15}{100}}=\frac{\frac{14}{100}}{\frac{14+15}{100}}=\frac{14}{100}\times \frac{100}{29}=\frac{14}{29}$