Question:

Given: Assume that the chances of a patient having a heart attack is 40%. It is also assumed 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.
Step 1: Formulate complete mathematical model:
Given problem statement:
$$Assume that the chances of a patient having a heart attack is 40%. It is also assumed that a meditation and yoga course reduces the risk of heart attack by 30% and prescription of certain drug reduces its chance by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga.$$
Establish the key governing equations and constraints:
$$P(E1)$$
[1.0 Mark]
Step 2: Set up primary equations / limits:
Writing the primary system or definite integral / matrix relation:
$$P(E1)$$
[1.0 Mark]
Step 3: Execute detailed intermediate reductions:
Performing step-by-step differentiation, integration, or matrix operations:
$$0.40 * 0.75$$
[1.0 Mark]
Step 4: Solve for critical variables / corner points / constants:
Evaluating the exact numerical coordinates, limits, or parameters:
$$14 / 29.$$
[1.0 Mark]
Step 5: Conclude and state complete final answer:
$$14 / 29.$$
Verify solution against problem constraints and state the final result. [1.0 Mark]
Conclusion: Problem solved completely.

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🎯 Official CBSE Marking Scheme:
Formulating mathematical model/constraints: 1.0 Mark
Setting up governing equations/integrals: 1.0 Mark
Executing intermediate calculations: 1.0 Mark
Evaluating exact parameters/corner points: 1.0 Mark
Stating final answer/optimal value: 1.0 Mark