If the probability of an event is P, then the probability of its completmentry event will be

Options

A. P-1
B. P
C. 1-P
D. `1-(1)/(P)`

Explanation

To solve the problem, we need to find the probability of the complementary event given that the probability of an event is \( P \).

### Step-by-Step Solution:

1. **Understanding the concept of complementary events**:
- The complementary event of an event \( A \) is the event that \( A \) does not occur. If the probability of event \( A \) occurring is \( P(A) = P \), then the probability of event \( A \) not occurring is \( P(A') \), where \( A' \) is the complementary event.

2. **Using the fundamental property of probabilities**:
- The sum of the probabilities of an event and its complementary event is always equal to 1. This can be expressed mathematically as:
\[ P(A) + P(A') = 1 \]

3. **Substituting the known probability**:
- Given that \( P(A) = P \), we can substitute this into the equation:
\[ P + P(A') = 1 \]

4. **Isolating the probability of the complementary event**:
- To find \( P(A') \), we rearrange the equation:
\[ P(A') = 1 - P \]

5. **Conclusion**:
- Therefore, the probability of the complementary event is:
\[ P(A') = 1 - P \]

### Final Answer:
The probability of the complementary event is \( 1 - P \).

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