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120. Two fair dice, one red and one blue, are rolled.
Let A be the event that the number rolled on the red die is odd.
Let B be the event that the number rolled on the blue die is odd.
Let C be the event that the sum of the numbers rolled on the two dice is odd.
Determine which of the following is true.
(A) A, B, and C are not mutually independent, but each pair is independent.
(B) A, B, and C are mutually independent.
(C) Exactly one pair of the three events is independent.
(D) Exactly two of the three pairs are independent.
(E) No pair of the three events is independent.
121. An urn contains four fair dice. Two have faces numbered 1, 2, 3, 4, 5, and 6; one has
faces numbered 2, 2, 4, 4, 6, and 6; and one has all six faces numbered 6. One of the dice
is randomly selected from the urn and rolled. The same die is rolled a second time.
Calculate the probability that a 6 is rolled both times.
(A) 0.174
(B) 0.250
(C) 0.292
(D) 0.380
(E) 0.417
122. An insurance agent meets twelve potential customers independently, each of whom is
equally likely to purchase an insurance product. Six are interested only in auto insurance,
four are interested only in homeowners insurance, and two are interested only in life
insurance.
The agent makes six sales.
Calculate the probability that two are for auto insurance, two are for homeowners
insurance, and two are for life insurance.
(A) 0.001
(B) 0.024
(C) 0.069
(D) 0.097
(E) 0.500