Q.Let $P(A) = \dfrac{3}{5}$ and $P(B) = \dfrac{1}{5}$. Find $P(A \cap B)$ if A and B are independent events.

Independence means $P(A\cap B)=P(A)\,P(B)=\dfrac{3}{5}\times\dfrac{1}{5}=\dfrac{3}{25}$.

In the TN HSC Class-11 Business Mathematics syllabus, two events $A$ and $B$ are independent when the occurrence of one does not affect the probability of the other; the multiplication rule for independent events then applies.

Step 1 — Recall the rule for independent events.

$P(A\cap B)=P(A)\times P(B).$

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