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: Key Formula for independent events:
For independent events, \(P(A\cap B)=P(A)\cdot P(B)\).

Step 2: Computing P(A∩B):
\(P(A\cap B)=0.3\times0.4=0.12\).

Step 3: Computing P(A∪B):
\(P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.3+0.4-0.12=0.58\).

Final Answer:
\[ \boxed{P(A\cap B)=0.12,\quad P(A\cup B)=0.58} \]