Question 4 A red die, a blue die, and a yellow die (all six-sided) are rolled. We are interested in the probability that the number appearing on the blue die is less than that appearing on the yellow die which is less than that appearing on the red die. (That is, if B (R) [Y ] is the number appearing on the blue (red) [yellow] die, then we are interested in P(B < Y < R). ) (a) What is the probability that no two of the dice land on the same number? (b) Given that no two of the dice land on the same number, what is the conditional probability that B < Y < R? (c) What is P(B < Y < R)?
Question 4 A red die, a blue die, and a yellow die (all six-sided) are rolled. We are interested in the probability that the number appearing on the blue die is less than that appearing on the yellow die which is less than that appearing on the red die. (That is, if B (R) [Y ] is the number appearing on the blue (red) [yellow] die, then we are interested in P(B < Y < R). ) (a) What is the probability that no two of the dice land on the same number? (b) Given that no two of the dice land on the same number, what is the conditional probability that B < Y < R? (c) What is P(B < Y < R)?
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter19: Probabilistic Dynamic Programming
Section19.4: Further Examples Of Probabilistic Dynamic Programming Formulations
Problem 3P
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Question 4 A red die, a blue die, and a yellow die (all six-sided) are rolled. We are interested in
the probability that the number appearing on the blue die is less than that appearing on the
yellow die which is less than that appearing on the red die. (That is, if B (R) [Y ] is the number
appearing on the blue (red) [yellow] die, then we are interested in P(B < Y < R). )
(a) What is the probability that no two of the dice land on the same number?
(b) Given that no two of the dice land on the same number, what is the
conditional probability that B < Y < R?
(c) What is P(B < Y < R)?
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