Question

If A and B are two independent events then $P\left(A\cap B\right)=$

1. $P\left(A\right)\cdot P\left(B\right)$
2. $P\left(A/B\right)$
3. $P\left(A\right)+P\left(B\right)$
4. $P\left(A\right)+P\left(B\right)-P\left(A\cup B\right)$

Answer: $P\left(A\right)\cdot P\left(B\right)$

Solution :-

Two events A and B are said to be independent, if P(A|B) = P(A) and P(B|A) = P(B), provided P(A) ≠ 0, P(B) ≠ 0.

By the multiplication rule of Probability,
P(A ∩ B) = P(A) · P(B|A) $\text{.........(1)}$

Now, if A and B are independent, then (1) become

P(A ∩ B) = P(A) · P(B)

So, correct answer is option-1, $\to P\left(A\right)\cdot P\left(B\right)$