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Problem 2
Two fair six-sided dice are rolled in succession. Complete the following, with all fractional values entered either in "p/q" form or as decimal values accurate to the nearest 0.001 .
(25%) With (1,3) denoting the values 1 on the first roll and 3 on the second, etc., check which of the possibilities below comprise the sample space.
(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)
(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)
(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)
(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)
(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)
(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)
(15%) Let A be the event that either a 6 or 3 is rolled first, followed by an odd number. Then P(A)=
(15%) Let B be the event that the sum of the two rolls is at most 6 . Then P(B)=
(15%) P(A∣∣B)=
(15%) Are A and B mutually exclusive events?
(pick one)
Why?
(pick one)
(15%) Are A and B independent events?
(pick one)
Why?
(pick one)
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