Question

I propose to you a game. You roll 2 dice. If the sum of the numbers...

I propose to you a game. You roll 2 dice. If the sum of the numbers showing is either 6, or 7, or 8, I win. If it is 2, 3, 4, 5, 9, 10, 11, 12, you win. Since you have lots more possible winning combinations than I do, the rules are that you pay me $2.00 when I win and I pay you $1.00 when you win. If we play this game 30 times, how much do you think you will win or lose? Explain why. You may wish to draw a histogram or create a table as an illustration in addition to showing your calculations.

Math   Statistics-And-Probability   
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Answer #1

If we roll 2 die then possible outcomes are:

Now we find how many times I win. That is getting sum 6, 7 and 8

Sum = 6, 5 times

Sum = 7, 6 times

Sum = 8, 5 times

Probability that I win is (5+6+5) / 36 = 16/36

So probability that you win = 1 - 16/36 = 20/36

Thus probability distribution of gain/ loss of you is,

x -2 1
P(X) 16 / 36 20 / 36

Expected gain or loss in one trail = = -2 * 16 /36 + 1 * 20/ 36 = - 1/3

Hence gain/ loss in 30 trails = 30 * (-1/3) = -10

Negative sign indicate loss.

Hence you will loss $ 10

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