Question

when one die is rolled, six outcomes are possible. these outcomes are those where the die shows each value between 1 and 6. complete parts (a) through (d). a = event the die comes up even b = event the die comes up 3 or more c = event the die comes up at most 3 d = event the die comes up 6 a. are events a and b mutually exclusive? a. yes. these events do not share any common outcomes. b. yes. at least the outcome where the die comes up 6 is common for these events. c. no. these events do not share any common outcomes. d. no. at least the outcome where the die comes up 6 is common for these events. b. are events b and c mutually exclusive? a. yes. these events do not share any common outcomes. b. no. at least the outcome where the die comes up 3 is common for these events. c. no. these events do not share any common outcomes. d. yes. at least the outcome where the die comes up 3 is common for these events. c. are events a, c, and d mutually exclusive? a. no. at least the outcome where the die comes up 2 is common for a and c. b. no. these events do not share any common outcomes. c. yes. these events do not share any common outcomes. d. yes. at least the outcome where the die comes up 2 is common for a and c.

Explanation:

Step1: Define mutually - exclusive events

Mutually - exclusive events have no common outcomes.

Step2: Analyze events A and B

Event A = {2, 4, 6}, Event B = {3, 4, 5, 6}. Since 4 and 6 are common outcomes, they are not mutually exclusive.

Step3: Analyze events B and C

Event B = {3, 4, 5, 6}, Event C = {1, 2, 3}. Since 3 is a common outcome, they are not mutually exclusive.

Step4: Analyze events A, C, and D

Event A = {2, 4, 6}, Event C = {1, 2, 3}, Event D = {6}. The outcome 2 is common for A and C, so they are not mutually exclusive.

Answer:

a. D. No. At least the outcome where the die comes up 6 is common for these events.
b. B. No. At least the outcome where the die comes up 3 is common for these events.
c. A. No. At least the outcome where the die comes up 2 is common for A and C.