The game of chuck-a-luck is played at carnivals in some parts of Europe. Its rules are as follows: if you pick a number from 1 to 6 and the operator rolls three dice. If the number you picked comes up on all three dice, the operator pays you £3; if it comes up on two dice, you are paid £2; and if it comes up on just one die, you are paid £1. Only if the number you picked does not come up at all, you pay the operator £1. The probability that you will win money playing in this game is:

You win money if your selected number appears on at least one die, which has a probability of 1 minus the probability of it not appearing at all. The probability of not appearing on any die is (5/6) cubed, equaling 125/216. Subtracting this from 1 gives 91/216, which equals approximately 0.42.

• Thanks
• Wrong explanation