Probability
Compound Probability
Grade 12
Question:
<p>\(P(E_1 \cap E_2) + P(E_2 \cap E_3) + P(E_3 \cap E_1)\) equals</p>
<p>(a) \(p_1(1 - p_2) + p_2(1 - p_3) + p_3(1 - p_1)\)</p>
<p>(b) \(p_1p_2 + p_2p_3 + p_3p_1\)</p>
<p>(c) \(p_1 + p_2 + p_3\)</p>
<p>(d) None of the above</p>
Step-by-Step Solution
Key Concept: Mutually exclusive events cannot occur simultaneously, so their intersections are empty
<p>Since $E_1$, $E_2$, and $E_3$ are mutually exclusive, their pairwise intersections are empty: $P(E_i \cap E_j) = 0$ for $i \neq j$. Therefore, the sum equals 0.</p>
Correct Answer: D