If `P(A)=0.3,P(B)=0.6` and A and B are independent events, then find the value of P(A and B).

Answer

To solve the problem, we need to find the probability of the intersection of two independent events A and B, denoted as P(A and B).

### Step-by-Step Solution:

1. **Understand the Given Information:**
- We are given:
- P(A) = 0.3
- P(B) = 0.6
- Events A and B are independent.

2. **Use the Formula for Independent Events:**
- For independent events, the probability of both events occurring together (the intersection) is given by:
\[ P(A \text{ and } B) = P(A) \times P(B) \]

3. **Substitute the Values:**
- Now, substitute the values of P(A) and P(B) into the formula:
\[ P(A \text{ and } B) = 0.3 \times 0.6 \]

4. **Calculate the Result:**
- Perform the multiplication:
\[ P(A \text{ and } B) = 0.18 \]

5. **Final Answer:**
- Therefore, the value of P(A and B) is:
\[ P(A \text{ and } B) = 0.18 \]