To calculate the expected value of your profit in this game of craps with the given conditions, we need to consider the probabilities and outcomes of winning and losing.
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Winning Probability: The probability of winning by betting on a sum of 3 is given as
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Losing Probability: The probability of losing is
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Profit if you win: If you win, you make a profit of $15.
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Loss if you lose: If you lose, you lose $1 (which is effectively a profit of -$1).
Now we can calculate the expected value
Substituting the values we have:
Calculating each term:
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Winning term:
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Losing term:
Now we add the two results to find the expected value:
Rounding to two decimal places, the expected value of your profit is:
Thus, the expected value of your profit is -0.11.