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Dice is a popular game in gambling casinos. Two dice are tossed, and various amounts are paid according to the outcome. In a certain game, if a twelve or five occurs on the first roll, the player wins. What is the probability of winning on the first roll?

  • math -

    The first dice generates a random integer between 1 and 6, and the second one does likewise - which gives 36 possible outcomes, all of which are equally likely if you distinguish between the two dice. Of these, how many total 5 or 12? There's only one way to get 12, namely that both dice come up six; however there are four different ways to get a total of 5, namely (1 & 4), (2 & 3), (3 & 2) and (4 & 1) for the first and second dice respectively. All of these outcomes are equally likely and are mutially exclusive, so all you have to do is add up the total number of them. That's (1 + 4) = 5 out of 36. 5/36 = 0.139, which is the answer.

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