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Probability

Conditional Probability and Independence

Grade None

Question:

<p>If \(A\) and \(B\) are mutually exclusive events with \(P(A) = 0.5\), \(P(B) = 0.3\), which are TRUE?</p>

A

B

C

D

Step-by-Step Solution

Key Concept: Mutually exclusive ⟹ P(A\capB)=0. Independent requires P(A\capB)=P(A)P(B)=0.15\neq0, so not independent.

<p><strong>A:</strong> \(P(A\cup B)=0.5+0.3=0.8\) ✓.</p><p><strong>B:</strong> Mutually exclusive \to \(P(A\cap B)=0\) ✓.</p><p><strong>C:</strong> \(P(A)P(B)=0.15\neq0=P(A\cap B)\) \to not independent. ✗.</p><p><strong>D:</strong> \(P(\bar A\cap\bar B)=1-0.8=0.2\) ✓.</p><p>Answer: ABD ✓.</p>

Correct Answer: ABD