Two independent events A and B will happen simultaneously, the probability is

Options

A. `P(A)+P(B)`
B. `P(overline(A)).P(overline(B))`
C. `P(A).P(B)`
D. `P(A)-P(B)`

Answer

To find the probability that two independent events A and B will happen simultaneously, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Independent Events**:
- Two events A and B are said to be independent if the occurrence of one event does not affect the occurrence of the other event.

2. **Identify the Probabilities of Events A and B**:
- Let \( P(A) \) be the probability of event A occurring.
- Let \( P(B) \) be the probability of event B occurring.

3. **Use the Formula for Independent Events**:
- For independent events, the probability that both events A and B occur simultaneously is given by the formula:
\[ P(A \text{ and } B) = P(A) \times P(B) \]

4. **Calculate the Probability**:
- Substitute the known values of \( P(A) \) and \( P(B) \) into the formula to find the required probability.

### Example Calculation:
- If \( P(A) = 0.5 \) and \( P(B) = 0.3 \), then:
\[ P(A \text{ and } B) = P(A) \times P(B) = 0.5 \times 0.3 = 0.15 \]

### Final Answer:
- The probability that both independent events A and B will happen simultaneously is \( P(A) \times P(B) \).

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