Question

If \(A\) and \(B\) are independent events and \(P(A)=0.3\), \(P(B)=0.4\), then find (i) \(P(A\cap B)\), (ii) \(P(A\cup B)\).

Hint:

Use P(A∩B)=P(A)P(B) for independent events, then the addition rule.

Answer 1

Step 1: Independence rule:
Independence directly gives \(P(A\cap B)=P(A)P(B)=0.3\times0.4=0.12\).

Step 2: General addition rule:
\(P(A\cup B)=P(A)+P(B)-P(A\cap B)\) always holds, regardless of independence.

Step 3: Substituting values:
\(P(A\cup B)=0.3+0.4-0.12=0.58\).

Final Answer:
\[ \boxed{0.12 \text{ and } 0.58} \]