You roll 5 fair 6-sided dice. Let C be the event that there are exactly 3 dice that are showing the same number. Let D be the event that there is at least one number i, 1 ≤ i ≤ 6, such that exactly 2 of the 6 dice are showing i. a) What is Pr(C)? b) What is Pr(D)? c) What is Pr(C ∪ D)? d) Are events C and D independent? In other words, is Pr(C ∩ D) = Pr(C) · Pr(D)?

You roll 5 fair 6-sided dice. Let C be the event that there are exactly 3 dice that are showing the same number. Let D be the event that there is at least one number i, 1 ≤ i ≤ 6, such that exactly 2 of the 6 dice are showing i. a) What is Pr(C)? b) What is Pr(D)? c) What is Pr(C ∪ D)? d) Are events C and D independent? In other words, is Pr(C ∩ D) = Pr(C) · Pr(D)?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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