If A and B are independent events such that `P(A)=(3)/(10),P(B)=(2)/(5)`, then P(A and B) is _______.

Answer

To find the probability of the intersection of two independent events A and B, we can use the formula:

\[ P(A \cap B) = P(A) \times P(B) \]

Given:
- \( P(A) = \frac{3}{10} \)
- \( P(B) = \frac{2}{5} \)

Now, we can substitute the values into the formula:

1. **Step 1: Calculate the product of the probabilities.**
\[ P(A \cap B) = P(A) \times P(B) = \frac{3}{10} \times \frac{2}{5} \]

2. **Step 2: Multiply the fractions.**
\[ P(A \cap B) = \frac{3 \times 2}{10 \times 5} = \frac{6}{50} \]

3. **Step 3: Simplify the fraction.**
\[ P(A \cap B) = \frac{6}{50} = \frac{3}{25} \]

Thus, the probability \( P(A \cap B) \) is \( \frac{3}{25} \).

### Final Answer:
\( P(A \cap B) = \frac{3}{25} \)

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