A fair six-sided die is rolled twice. Let X be the number showing on the first roll and A be the event "at least one odd number is rolled". Find (a) The probability P(A) of the event A, (b) The probability that the first number rolled is a 2, given that at least one odd number is rolled (this is the conditional probability P({X = 2}|A)), (c) The probability mass function of X given that at least one odd number is rolled (this is the pmf of X conditional on A), (d) The average value of this distribution, which is the conditional expectation E(X|A).

A fair six-sided die is rolled twice. Let X be the number showing on the first roll and A be the event "at least one odd number is rolled". Find (a) The probability P(A) of the event A, (b) The probability that the first number rolled is a 2, given that at least one odd number is rolled (this is the conditional probability P({X = 2}|A)), (c) The probability mass function of X given that at least one odd number is rolled (this is the pmf of X conditional on A), (d) The average value of this distribution, which is the conditional expectation E(X|A).

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.2: Probability

Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...

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