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

Options

A. `0*6`
B. `0*5`
C. `0*7`
D. none

Answer

To find the probability of neither event A nor event B occurring, we can follow these steps:

### Step 1: Understand the probabilities given
We know:
- Probability of event A occurring, P(A) = 0.5
- Probability of event B occurring, P(B) = 0.3
- Events A and B are mutually exclusive, which means they cannot occur at the same time.

### Step 2: Calculate the probability of either A or B occurring
Since A and B are mutually exclusive, the probability of either A or B occurring is given by the sum of their individual probabilities:
\[ P(A \cup B) = P(A) + P(B) \]
Substituting the values:
\[ P(A \cup B) = 0.5 + 0.3 = 0.8 \]

### Step 3: Calculate the probability of neither A nor B occurring
The probability of neither A nor B occurring is the complement of the probability of either A or B occurring. This can be calculated as:
\[ P(\text{neither A nor B}) = 1 - P(A \cup B) \]
Substituting the value we found in Step 2:
\[ P(\text{neither A nor B}) = 1 - 0.8 = 0.2 \]

### Final Answer
The probability of neither A nor B occurring is **0.2**.

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