To calculate the expected value of the game, you multiply each possible outcome by its probability and sum them up. In this case, the expected value is -$0.50, which means that the player can expect to lose $0.50 per game, on average.
The expected value of a game is a measure of what a player can expect to win or lose on average over many repetitions of the game. To calculate the expected value, you multiply each possible outcome by its probability and sum them up.
In this case, the player pays $3 to roll two dice. If they roll a sum of 4, they win $12, and if they roll a sum of 6, they win $6. We need to use the probability distribution to compute the expected value.
Let's calculate:
Probability distribution:
P(sum of 4) = $rac{3}{36}$ = $rac{1}{12}$
P(sum of 6) = $rac{5}{36}$
Expected value = ($12 imes rac{1}{12}$) + ($6 imes rac{5}{36}$) - ($3 imes 1$
Expected value = $1 + rac{5}{2} - 3$ = $-0.5$.
The expected value of the game is -$0.50, which means that, on average, the player can expect to lose $0.50 per game.