Solution #55: Carnival Dice

The game is fair and does not favor either you or the carnival. The chart shows the eleven winning and twenty-five losing combinations for betting on the number 1. One outcome will win $5 for you, ten will win $2, and twenty-five will lose $1. Since these outcome are all equally likely, your expected winnings are:

($2 x 10) + ($5 x 1) - ($1 x 25) = 0

    1   2   3   4   5   6
1  1,1 1,2 1,3 1,4 1,5 1,6---
2  2,1 2,2 2,3 2,4 2,5 2,6 L
3  3,1 3,2 3,3 3,4 3,5 3,6 O
4  4,1 4,2 4,3 4,4 4,5 4,6 S
5  5,1 5,2 5,3 5,4 5,5 5,6 E
6  6,1 6,2 6,3 6,4 6,5 3,6 |
   WIN |---------LOSE------+

Source: Mathematics Teacher
Categories: Probability

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