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STA 112 Quantifying Uncertainty Objective Question
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Question

How does the Multiplication Rule extend to three events, E1, E2, and E3, according to Slide 16?
Options
A P(E<sub>1</sub>E<sub>2</sub>E<sub>3</sub>) = P(E<sub>1</sub>)P(E<sub>2</sub>)P(E<sub>3</sub>)
B P(E<sub>1</sub>E<sub>2</sub>E<sub>3</sub>) = P(E<sub>1</sub>) + P(E<sub>2</sub>) + P(E<sub>3</sub>)
C P(E<sub>1</sub>E<sub>2</sub>E<sub>3</sub>) = P(E<sub>1</sub>)P(E<sub>2</sub>|E<sub>1</sub>)P(E<sub>3</sub>|E<sub>1</sub>E<sub>2</sub>)
Correct Answer
D P(E<sub>1</sub>E<sub>2</sub>E<sub>3</sub>) = P(E<sub>1</sub>E<sub>2</sub>) + P(E<sub>2</sub>E<sub>3</sub>) + P(E<sub>1</sub>E<sub>3</sub>)
Correct Answer

Option C is the correct answer.

Detailed Explanation

Slide 16 shows the extension: P(E1E2E3) = P(E1)P(E2|E1)P(E3|E1E2).

Hint

Remember that the Multiplication Rule involves conditional probabilities for sequential events.

Question Info

Course: STA 112
Topic: Quantifying Uncertainty
Type: Objective
Difficulty: Not specified
Question 53 of 112
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