Question:

Given: Suppose 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.
Step 1: Formulate complete mathematical model:
Given problem statement:
$$Suppose 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.$$
Establish the key governing equations and constraints:
$$P(M)$$
[1.0 Mark]
Step 2: Set up primary equations / limits:
Writing the primary system or definite integral / matrix relation:
$$P(M)$$
[1.0 Mark]
Step 3: Execute detailed intermediate reductions:
Performing step-by-step differentiation, integration, or matrix operations:
$$0.0025. P(M|G)$$
[1.0 Mark]
Step 4: Solve for critical variables / corner points / constants:
Evaluating the exact numerical coordinates, limits, or parameters:
$$20 / 21.$$
[1.0 Mark]
Step 5: Conclude and state complete final answer:
$$20 / 21.$$
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