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)?
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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Question
You roll 5 fair 6-sided dice. Let C be the
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)?
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