If A and B are two independent events such that
`P(A)=(5)/(13),P(B)=(2)/(13)`, then` P (A cap B)`is equal to __________.

Options

A. `(10)/(169)`
B. `(5)/(169)`
C. `(2)/(169)`
D. `(11)/(169)`

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:
- \( P(A) = \frac{5}{13} \)
- \( P(B) = \frac{2}{13} \)

Now, let's calculate \( P(A \cap B) \):

1. Substitute the values of \( P(A) \) and \( P(B) \) into the formula:
\[ P(A \cap B) = \left(\frac{5}{13}\right) \times \left(\frac{2}{13}\right) \]

2. Multiply the numerators:
\[ 5 \times 2 = 10 \]

3. Multiply the denominators:
\[ 13 \times 13 = 169 \]

4. Combine the results:
\[ P(A \cap B) = \frac{10}{169} \]

Thus, the probability \( P(A \cap B) \) is equal to \( \frac{10}{169} \).

**Final Answer:**
\[ P(A \cap B) = \frac{10}{169} \]

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