Question

Two fair die are tossed, and the uppermost face of each die is observed. The following events are defined from this random experiment:

AA represent the event the uppermost faces sum to five

BB represent the event that the product of the uppermost faces is four. For example, die1*die2 = 4

CC represent the event that the absolute difference between the uppermost faces is 1. For example, |die1−die2|=1|die1−die2|=1

Part (a) Find the probability that the uppermost faces do not sum to five.

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(Use four decimals in your answer)

Part (b) Find P(A∪C)P(A∪C)

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(Use four decimals)

Part (c) What is the probability that the uppermost faces do not sum to five or are not a product of 4?

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(use four decimals)

Part (d) Find P(A∩(B∪C))P(A∩(B∪C))

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(use four decimals)

Part (e) Are the events a sum of 5 and a product of 4 mutually exclusive events? Select the most appropriate reason below.
A. A sum of 5 and a product of 4 are not mutually exclusive events because P(A∩B)=P(A)P(B)P(A∩B)=P(A)P(B).
B. A sum of 5 and a product of 4 are not mutually exclusive events because P(A∩B)≠0P(A∩B)≠0.
C. A sum of 5 and a product of 4 are mutually exclusive events because they are not independent events.
D. A sum of 5 and a product of 4 are not mutually exclusive events because P(A∩B)≠P(A)P(B)P(A∩B)≠P(A)P(B).
E. A sum of 5 and a product of 4 are mutually exclusive events because P(A∩B)=0P(A∩B)=0.

Answer 1