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 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?

Explanation

To solve the problem, we will use Bayes' theorem to find the probability that a patient followed a course of meditation and yoga given that they suffered a heart attack.

### Step-by-step Solution:

1. **Define Events**:
- Let \( A \) be the event that the patient followed meditation and yoga.
- Let \( A' \) be the event that the patient followed the prescribed drug.
- Let \( B \) be the event that the patient suffers a heart attack.

2. **Given Probabilities**:
- The probability of a patient having a heart attack without any intervention is \( P(B) = 0.4 \).
- The probability of a heart attack after meditation and yoga is reduced by 30%, so:
\[ P(B|A) = P(B) \times (1 - 0.3) = 0.4 \times 0.7 = 0.28 \]
- The probability of a heart attack after taking the prescribed drug is reduced by 25%, so:
\[ P(B|A') = P(B) \times (1 - 0.25) = 0.4 \times 0.75 = 0.3 \]

3. **Prior Probabilities**:
- Since the patient can choose either option with equal probability:
\[ P(A) = P(A') = \frac{1}{2} \]

4. **Using Bayes' Theorem**:
We want to find \( P(A|B) \):
\[ P(A|B) = \frac{P(A) \cdot P(B|A)}{P(A) \cdot P(B|A) + P(A') \cdot P(B|A')} \]

5. **Substituting Values**:
Substitute the values we calculated:
\[ P(A|B) = \frac{\frac{1}{2} \cdot 0.28}{\frac{1}{2} \cdot 0.28 + \frac{1}{2} \cdot 0.3} \]

6. **Simplifying**:
\[ P(A|B) = \frac{0.14}{0.14 + 0.15} = \frac{0.14}{0.29} \]

7. **Final Calculation**:
\[ P(A|B) = \frac{14}{29} \]

Thus, the probability that the patient followed a course of meditation and yoga given that they suffered a heart attack is \( \frac{14}{29} \).