The probability of an event A occurring is 0.5 and of B is 0.3. If A and B are mutually exclusive events then the probability of neither A nor B occurring is

Options

A. `0.2`
B. `0.3`
C. `0.5`
D. `0.8`

Answer

To solve the problem, we need to find the probability of neither event A nor event B occurring, given that the probability of event A is 0.5 and the probability of event B is 0.3, and that A and B are mutually exclusive events.

### Step-by-Step Solution:

1. **Identify the probabilities of events A and B:**
- Probability of A, \( P(A) = 0.5 \)
- Probability of B, \( P(B) = 0.3 \)

2. **Calculate the probability of A union B (i.e., either A or B occurring):**
- Since A and B are mutually exclusive, the probability of A union B is given by:
\[ P(A \cup B) = P(A) + P(B) \]
- Substitute the values:
\[ P(A \cup B) = 0.5 + 0.3 = 0.8 \]

3. **Determine the probability of neither A nor B occurring:**
- The probability of neither A nor B occurring can be expressed as:
\[ P(\text{neither A nor B}) = 1 - P(A \cup B) \]
- Substitute the value of \( P(A \cup B) \):
\[ P(\text{neither A nor B}) = 1 - 0.8 = 0.2 \]

4. **Final Result:**
- The probability of neither A nor B occurring is:
\[ P(\text{neither A nor B}) = 0.2 \]

### Summary:
The probability of neither event A nor event B occurring is 0.2.

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