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STA 112 Quantifying Uncertainty Objective Question
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Question

The derivation of the Complement Rule, P(Ec) = 1 - P(E), relies on which of the three axioms of probability?
Options
A Only Axiom 1 (Non-negativity).
B Only Axiom 2 (Probability of the Sample Space).
C Axiom 2 (P(S)=1) and Axiom 3 (Additivity for Disjoint Events).
Correct Answer
D All three axioms are required for the derivation.
Correct Answer

Option C is the correct answer.

Detailed Explanation

Slide 8 shows the derivation: E and Ec are mutually exclusive, and their union is S. Therefore, P(S) = P(E ∪ Ec) = P(E) + P(Ec) (using Axiom 3). Since P(S) = 1 (Axiom 2), we get 1 = P(E) + P(Ec), which leads to the complement rule.

Hint

Consider how E and Ec relate to the sample space and how their probabilities combine.

Question Info

Course: STA 112
Topic: Quantifying Uncertainty
Type: Objective
Difficulty: Not specified
Question 49 of 112
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