If A and B are two independent events with `P(A) = 3/5 and P(B) =4/9` then `P(A cap B)` is equal to:

Options

A. `4/15`
B. `8/45`
C. `1/3`
D. `2/9`

Answer

To find the probability of the intersection of two independent events A and B, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We are given that the probability of event A, \( P(A) = \frac{3}{5} \).
- We are also given that the probability of event B, \( P(B) = \frac{4}{9} \).
- Events A and B are independent.

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

3. **Substitute the Given Probabilities**:
- Substitute the values of \( P(A) \) and \( P(B) \) into the formula:
\[ P(A \cap B) = \frac{3}{5} \times \frac{4}{9} \]

4. **Multiply the Fractions**:
- To multiply the fractions, multiply the numerators and the denominators:
\[ P(A \cap B) = \frac{3 \times 4}{5 \times 9} = \frac{12}{45} \]

5. **Simplify the Result**:
- Now, simplify \( \frac{12}{45} \):
- Both the numerator and denominator can be divided by 3:
\[ \frac{12 \div 3}{45 \div 3} = \frac{4}{15} \]

6. **Final Answer**:
- Therefore, the probability of the intersection of events A and B is:
\[ P(A \cap B) = \frac{4}{15} \]