Alice and finn roll two number cubes. which of the following rules will make the game fair?
a. alice wins if a total of 5 is rolled. finn wins if a total of 9 is rolled.
b. alice wins if a total of 7 is rolled. finn wins if a total of 8 is rolled.
c. alice wins if a total of 3 is rolled. finn wins if a total of 10 is rolled.
d. alice wins if a total of 4 is rolled. finn wins if a total of 11 is rolled.

The correct answer is option'A':  Alice wins if a total of 5 is rolled. Finn wins if a total of 9 is rolled.

Explanation:

Since the sample outcomes of both the experiments are the same we have

1) Alice will win if the total of 5 is rolled thus the following cases are valid:

i) Alice gets 1 Finn gets 4.

ii)Alice gets 4 Finn gets 1.

iii)Alice gets 2 Finn gets 3.

iv)Alice gets 3 Finn gets 2.

Thus the cases in favor of Alice are 4.

2) Finn will win if the total of 9 is rolled thus the following cases are valid:

i) Alice gets 3 Finn gets 6.

ii)Alice gets 6 Finn gets 3.

iii)Alice gets 4 Finn gets 5.

iv)Alice gets 5 Finn gets 4.

Thus the cases in favor of Finn are 4.

Thus both have equal opportunities to succeed.

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