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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:
There are 3 ways to win money in the game.
The number you picked can come up in one dice, 2 dice or 3 dice.
The probability of the number you picked coming in all three dice = (1/6)*(1/6)*(1/6) = 1/216
The probability of the number picked coming on 2 dice = 3C2*(5/6)(1/6)(1/6) = 15/216
The probability of the number picked coming on 1 dice = 3C1*(5/6)(5/6)(1/6) = 75/216
Probability of winning = 1/216 + 15/214 + 75/216 = 91/216 = 0.421.
Therefore, option C is the right answer.
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