Strange Dice.
Two players, Marcy and Jonas, have 2 unconventional dice. One red die which has four sides with the number 3, one side with the number 4, and one side side with the number 1. The other die is green and has three sides with the number 2, two sides with the number 5, and one side with the number 3. If Jonas plays with the red die and Marcy plays with the green die. If whoever rolls the highest number wins, who has better chances of winning?
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P(Marcy wins)
= Sigma{P(Marcy rolls a number N) × P(Jonas rolls a number less than N)}
= (3/6)(1/6) + (2/6)(6/6) + (1/6)(1/6)
= (3 + 12 + 1) / 36
= 16 / 36
= 4/9
P(Jonas wins)
= Sigma{P(Jonas rolls a number N) × P(Marcy rolls a number less than N)}
= (4/6)(3/6) + (1/6)(4/6) + (1/6)(0/6)
= (12 + 4 + 0) / 36
= 16 / 36
= 4/9
P(Jonas wins) = P(Marcy wins)