Mark the correct alternative in the following question:

$If the events A and B are independent, then P (A \cap B) is equal to (a) P (A) + P (B) (b) P (A) - P (B) (c) P (A) P (B) (d) \frac{P (A)}{P (B)}$

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Solution

$As, A and B are independent events . So, P (A | B) = P (A) and P (B | A) = P (B) Now, P (A | B) = \frac{P (A \cap B)}{P (B)} \Rightarrow P (A \cap B) = P (B) P (A | B) \Rightarrow P (A \cap B) = P (B) P (A)$

Hence, the correct alternative is option (c).

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