Question

suppose you play a game where you roll a set of 2 fair dice. if you roll a 4, 5, or 6, you will lose $6, but if you roll anything else, then you win $3. how much money will you gain or lose per each throwing?

Answer 1

The outcome of rolling a set of 2 fair dice is a number between 2 and 12, and there is a probability of 1/9 for each outcome.

For the outcomes 4,5,6, you will lose $6, and for the other outcomes, you will win $3.

There are 3 outcomes 4,5,6, and 9-3 = 6 outcomes where you win $3.

So your expected gain/loss per roll is:

(3/9) * $3 + (3/9) * (-$6) = -$1

Therefore, on average, you will lose $1 per each throwing.