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You roll a fair six-sided die twice. Let A be the event that the first roll is odd, B be the event that you roll at least one “six”, and C be the event that the sum of the rolls is seven. (a) Are the events A and B independent? (b) Are the events A, B, and C mutually independent? (c) Are the events A and B conditionally independent given C?

You roll a fair six-sided die twice. Let A be the event that the first roll is odd, B be the event that you roll at least one “six”, and C be the event that the sum of the rolls is seven. (a) Are the events A and B independent? (b) Are the events A, B, and C mutually independent? (c) Are the events A and B conditionally independent given C?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 19E
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You roll a fair six-sided die twice. Let A be the event that the first roll is odd, B be the event that you roll at least one “six”, and C be the event that the sum of the rolls is seven.

(a) Are the events A and B independent?
(b) Are the events A, B, and C mutually independent?

(c) Are the events A and B conditionally independent given C?

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