Let A and B be independent events such that P(A)=0.6 and P(B)=0.7 find `P(A nn overset-B)`.

Options

A. 0.18
B. 0.56
C. 0.36
D. 0.76

Answer

To solve the problem, we need to find \( P(A \cap B') \), where \( B' \) is the complement of event \( B \). Given that events \( A \) and \( B \) are independent, we can use the properties of independent events to find the required probability.

### Step-by-Step Solution:

1. **Identify the Given Probabilities**:
- \( P(A) = 0.6 \)
- \( P(B) = 0.7 \)

2. **Calculate the Probability of the Complement of B**:
- The probability of the complement of event \( B \) is given by:
\[ P(B') = 1 - P(B) = 1 - 0.7 = 0.3 \]

3. **Use the Independence of Events A and B**:
- Since \( A \) and \( B \) are independent, the probability of the intersection of \( A \) and \( B' \) can be calculated as:
\[ P(A \cap B') = P(A) \cdot P(B') \]

4. **Substitute the Known Values**:
- Now substitute the values we have:
\[ P(A \cap B') = P(A) \cdot P(B') = 0.6 \cdot 0.3 \]

5. **Calculate the Final Probability**:
- Performing the multiplication gives:
\[ P(A \cap B') = 0.6 \cdot 0.3 = 0.18 \]

Thus, the final answer is:
\[ P(A \cap B') = 0.18 \]