You and your best friend decide to play a game of chance with dice. There are tw

Question

You and your best friend decide to play a game of chance with dice. There are two dice. One green and one yellow. The green dice is not well balanced so it gives you a chance of 1/3 of getting a 6 and an equal chance on the remaining numbers. The yellow dice is normal. Your friend gives you the choice of playing with the green or yellow dice. The game now goes like this. You roll your dice and your friend rolls hers. Whomever has the highest number wins. If the numbers are the same, the player with the yellow dice

Explanation / Answer

For green dice,

P(1) = P(2) = P(3) = P(4) = P(5) = (1- (1/3))/5 = 2/15

P(6) = 1/3

Green dice will win over yellow dice for the following events:

(2,1), (3,1) ,(3,2) , (4,1) , (4,2) , (4,3) , (5,1) , (5,2) , (5,3) , (5,4) , (6,1), (6,2) , (6,3) , (6,4), (6,5)

where (x,y) denotes Green has x number and Yellow has y number.

Probability that green will win = 10*(2/15)*(1/6) + 5*(1/3)*(1/6) = 0.5

So it does not make a difference whether yellow dice is chosen or green dice is chosen.

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