You have two six-sided dice. Die A has 2 twos, 1 three, 1 five, 1 ten, and 1 fou

Question

You have two six-sided dice. Die A has 2 twos, 1 three, 1 five, 1 ten, and 1 fourteen on its faces. Die B has a one, a three, a five, a seven, a nine, and an eleven on its faces.

B. On any given roll of both dice, what is the probability that the number showing on die A will be greater than the number on die B? What is the probability that the number showing on die B will be greater?

C. Considering your answers for parts A and B, which die would you choose to roll, and why, if your goal was (i) to achieve a higher score than an opponent rolling the other die, and (ii) to achieve the highest possible score on a single roll of the die?

Explanation / Answer

Solution:

B) The sample space is: (for A and B)
(2,1) (3,1) (5,1) (10,1) (14,1)
(2,3) (3,3) (5,3) (10,3) (14,3)
(2,5) (3,5) (5,5) (10,5) (14,5)
(2,7) (3,7) (5,7) (10,7) (14,7)
(2,9) (3,9) (5,9) (10,9) (14,9)
(2,11) (3,11) (5,11) (10,11) (14,11)
30 points in sample space:
number of rolls in which A > B = 16
P( A > B) = 16/30 = 8/15
P( B > A) = 13/30

C) A (since there are 16 numbers in A > B), but only 13 numbers in B > A.

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