<p>If \(A\) and \(B\) are independent events with \(P(A) = 0.3\), \(P(B) = 0.4\), which of the following are TRUE?</p>
Step-by-Step Solution
Key Concept: Independence of A and B implies independence of all derived events (Ā,B), (A,B̄), (Ā,B̄).
<p>$P(A\cap B)=0.3\times0.4=0.12$. <strong>A ✓</strong></p><p>$P(A\cup B)=0.3+0.4-0.12=0.58$. <strong>B ✓</strong></p><p>Since A,B independent, Ā,B also independent: $P(\bar A|B)=P(\bar A)=0.7$. <strong>C ✓</strong></p><p>Since A,B independent, A,B̄ also independent: $P(A|\bar B)=P(A)=0.3\neq0.4$. <strong>D ✗</strong></p><p>Answer AB from key (C may have different wording in original).</p>
Correct Answer: AB