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Consider independently rolling two fair dice, one red and

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 82E Chapter 2

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 82E

Consider independently rolling two fair dice, one red and the other green. Let ?A be the event that the red die shows 3 dots, ?B ?be the event that the green die shows 4 dots, and ?C ?be the event that the total number of dots showing on the two dice is 7. Are these events pairwise independent (i.e., are ?A ?and ?B ?independent events, are A ?and ?C ?independent, and are ?B ?and ?C ?independent)? Are the three events mutually independent?

Step-by-Step Solution:

Answer Step 1 of 6 The probability of each of these events is 1/6. P(A)=, P(B)=, P(c)=1/6 If P(A B) = P(A)*P(B), then the events A and B are independent. Step 2 of 6 A and B are plainly independent events. P(A & B) = 1/36 = (1/6) (1/6) = P(A) P(B) Step 3 of 6 Finding P(A C). the possible outcomes of C are {C} = {(R=3,G=4), (R=4,G=3), (R=2,G=5), (R=5,G=2), (R=1,G=6), (R=6,G=1)}. event A is defined as R=3 in the set of possible outcomes for C {A C} = {(R=3,G=4)}. Now P(A C) = P(R=3)*P(G=4) = P(A)*P(B) = (1/6)*(1/6) = 1/36.

Step 4 of 6

Chapter 2, Problem 82E is Solved
Step 5 of 6

Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

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Consider independently rolling two fair dice, one red and

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