Probability
Compound Probability
Grade 12
Question:
<p>\(P(\text{none of } E_1, E_2, E_3)\) equals</p>
<p>(a) \(1 - p_1 - p_2 - p_3\)</p>
<p>(b) \(p_1 + p_2 + p_3\)</p>
<p>(c) \((1 - p_1)(1 - p_2)(1 - p_3)\)</p>
<p>(d) None of the above</p>
Step-by-Step Solution
Key Concept: For mutually exclusive events, the probability of none occurring is the product of individual non-occurrence probabilities
<p>Since $E_1$, $E_2$, and $E_3$ are mutually exclusive, the probability that none occurs is: $P(\text{none}) = (1 - p_1)(1 - p_2)(1 - p_3)$</p>
Correct Answer: C