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STA 112 Quantifying Uncertainty Objective Question
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Question

If events E1, E2, ... are mutually exclusive, what does the Additivity for Disjoint Events axiom state about their probabilities?
Options
A P(∪<sup>∞</sup><sub>n=1</sub> E<sub>n</sub>) = P(E<sub>1</sub>) + P(E<sub>2</sub>)
B P(∪<sup>∞</sup><sub>n=1</sub> E<sub>n</sub>) = 1
C P(∪<sup>∞</sup><sub>n=1</sub> E<sub>n</sub>) = Σ<sup>∞</sup><sub>n=1</sub> P(E<sub>n</sub>)
Correct Answer
D P(∪<sup>∞</sup><sub>n=1</sub> E<sub>n</sub>) = 0
Correct Answer

Option C is the correct answer.

Detailed Explanation

According to Slide 7, the third axiom 'Additivity for Disjoint Events' states: P(∪∞n=1 En) = Σ∞n=1 P(En) if E1, E2, ... are mutually exclusive.

Hint

This axiom deals with the probability of the union of many disjoint events.

Question Info

Course: STA 112
Topic: Quantifying Uncertainty
Type: Objective
Difficulty: Not specified
Question 19 of 112
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