What is the sum of the probabilities of happeing of an event & not happening of the event ?

Answer

To find the sum of the probabilities of an event happening and not happening, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Event**: Let’s denote an event as \( A \). The probability of event \( A \) happening is represented as \( P(A) \).

2. **Define the Complement of the Event**: The event that \( A \) does not happen is called the complement of \( A \), denoted as \( A' \) or \( A^c \). The probability of the event not happening is represented as \( P(A') \).

3. **Understanding the Sum of Probabilities**: According to the basic principles of probability, the sum of the probability of an event and the probability of its complement is always equal to 1. This can be expressed mathematically as:
\[ P(A) + P(A') = 1 \]

4. **Conclusion**: Therefore, the sum of the probabilities of an event happening and not happening is:
\[ P(A) + P(A') = 1 \]

### Final Answer:
The sum of the probabilities of an event happening and not happening is always 1.

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