If C and D are two events such that `C subD`and P(D) ne0,` then the correct statement aomog the following is

Options

A. `P(C|D)=(P(D))/(P(D))`
B. `P(C|D)=P(C)`
C. `P(C|D)geP(C)`
D. `P(C|D)ltP(C)`

Explanation

To solve the question, we need to analyze the relationship between the events C and D, given that C is a subset of D (C ⊆ D) and that the probability of D is not equal to zero (P(D) ≠ 0).

### Step-by-Step Solution:

1. **Understanding the Relationship**:
Since C is a subset of D, this means that every outcome in event C is also in event D. Therefore, the intersection of C and D is just C itself:
\[ C \cap D = C \]

2. **Using the Definition of Conditional Probability**:
The conditional probability of C given D, denoted as P(C|D), is defined as:
\[ P(C|D) = \frac{P(C \cap D)}{P(D)} \]

3. **Substituting the Intersection**:
From step 1, we know that \(P(C \cap D) = P(C)\). Thus, we can substitute this into the conditional probability formula:
\[ P(C|D) = \frac{P(C)}{P(D)} \]

4. **Analyzing the Probability of D**:
Given that P(D) is not equal to zero and is less than or equal to 1 (0 < P(D) ≤ 1), we can deduce the following:
- Since P(D) is a positive number less than or equal to 1, dividing P(C) by P(D) will yield a value that is greater than or equal to P(C) because:
\[ P(C|D) = \frac{P(C)}{P(D)} \geq P(C) \]

5. **Conclusion**:
Therefore, we conclude that:
\[ P(C|D) \geq P(C) \]
This leads us to identify that option C is the correct statement.

### Final Answer:
The correct statement is:
**Option C: P(C|D) is greater than or equal to P(C)**.

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