Consider the dice A, B, and C below. The opposite sides have the same values as those shown.

A (2,9,4) B (1,8,6) C (3,7,5)

a) If A is rolled against B with the higher number the winner, which should you bet on? Why?

Explain in terms of probability.

b) What if B is rolled against C?

c) Now what about C against A?

a) A

b) B

c) C

Step-by-step explanation:

There are 9 different outcomes when 2 die are rolled.

a) A & B : A has a higher chance of winning, i. e probability of 5/9

(A, B) : (2,1) (9,1) (9,8) (9,6) (4,1)

In other 4 possible outcomes, B will win which is a probability of 4/9 (less than 5/9)

b) B & C: B has a higher chance of winning, i. e probability of 5/9

(B, C) : (8,3) (8,7) (8,5) (6,3) (6,5)

In other 4 possible outcomes, C will win which is a probability of 4/9 (less than 5/9)

c) A & C: C has a higher chance of winning, i. e probability of 5/9

(A, C) : (2,3) (2,7) (2,5) (4,7) (4,5)

In other possible outcomes, A will win which is a probability of 4/9 (less than 5/9)