We have to find:
(a) Probability that A is more likely to roll a higher number than B.
(b) Probability that B is more likely to roll a higher number than C.
(c) Probability that C is more likely to roll a higher number than A.
Solution:
· Dice A has sides 2, 2, 4, 4, 9, 9.
· Dice B has sides 1, 1, 6, 6, 8, 8.
· Dice C has sides 3, 3, 5, 5, 7, 7
(a) Probability that A is more likely to roll a higher number than B.
S= {(2, 1), (2, 6), (2, 8), (4, 1), (4, 6), (4, 8), (9, 1), (9, 6), (9, 8)}
S (A B) = {(2, 1), (4, 1), (9, 1), (9, 6), (9, 8)}
P (A B) =
(b) Probability that B is more likely to roll a higher number than C.
S= {(1, 3), (1, 5), (1, 7), (6, 3), (6, 5), (6, 7), (8, 3), (8, 5), (8, 7)}
S (B C) = {(6, 3), (6, 5), (8, 3), (8, 5), (8, 7)}
P (B C) =
(c) Probability that C is more likely to roll a higher number than A.
S= {(3, 2), (3, 4), (3, 9), (5, 2), (5, 4), (5, 9), (7, 2), (7, 4), (7, 9)}
S (C A) = {(3, 2), (5, 2), (5, 4), (7, 2), (7, 4)}
P (C A) =
The probability that A rolls a higher number than B, the probability that B rolls a higher than C, and the probability that C rolls a higher than A are all
P (A B) = P (B C) = P (C A) =