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

Options

A. 0.24
B. 0.16
C. 0.36
D. none of these

Answer

To solve the problem of finding \( P(A' \cap B) \), where \( A \) and \( B \) are independent events with \( P(A) = 0.6 \) and \( P(B) = 0.6 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the probability of the intersection of the complement of event \( A \) and event \( B \), denoted as \( P(A' \cap B) \).

2. **Find \( P(A') \)**: The complement of event \( A \) is given by:
\[ P(A') = 1 - P(A) \]
Substituting the value of \( P(A) \):
\[ P(A') = 1 - 0.6 = 0.4 \]

3. **Use Independence of Events**: Since events \( A \) and \( B \) are independent, the complement of \( A \) (i.e., \( A' \)) and event \( B \) are also independent. Therefore, we can use the multiplication rule for independent events:
\[ P(A' \cap B) = P(A') \cdot P(B) \]

4. **Substitute the Values**: Now we can substitute the values we have:
\[ P(A' \cap B) = P(A') \cdot P(B) = 0.4 \cdot 0.6 \]

5. **Calculate the Result**: Performing the multiplication:
\[ P(A' \cap B) = 0.4 \cdot 0.6 = 0.24 \]

### Final Answer:
Thus, the probability \( P(A' \cap B) \) is \( 0.24 \).

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