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STA 112 Quantifying Uncertainty Objective Question
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Question

The Law of Total Probability is used to calculate P(E) when the sample space S is partitioned by mutually exclusive and exhaustive events F1, F2, ..., Fn. Which formula correctly represents this law?
Options
A P(E) = P(E|F<sub>1</sub>) + P(E|F<sub>2</sub>) + ... + P(E|F<sub>n</sub>)
B P(E) = Σ P(E|F<sub>i</sub>)P(F<sub>i</sub>)
Correct Answer
C P(E) = P(E) / P(F<sub>i</sub>)
D P(E) = P(F<sub>i</sub>|E)P(F<sub>i</sub>)
Correct Answer

Option B is the correct answer.

Detailed Explanation

Slide 22 presents the Law of Total Probability as: 'P(E) = Σi=1n P(E|Fi)P(Fi)'.

Hint

This law calculates the overall probability of an event by considering all possible 'causes' or conditions under which it can occur, weighted by their probabilities.

Question Info

Course: STA 112
Topic: Quantifying Uncertainty
Type: Objective
Difficulty: Not specified
Question 42 of 112
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