Question

A player pays $3 to play the following game: He rolls a die and receives $7 if he tosses a 6 and $1 for anything

else. Find the player's expected net winnings for the game.

Answer 1

Calculate the expected value using the probabilities and outcomes of the game. In this case, the player pays $3 to play and can win $7 for rolling a 6 or $1 for any other outcome. The expected net winnings for the game are $1.167.

Step-by-step explanation:

To find the player's expected net winnings for the game, we need to calculate the expected value. The expected value is the sum of the products of each outcome and its probability. In this game, the player pays $3 to play and can win $7 if they roll a 6 or $1 for any other outcome. Let's calculate the expected value:

Expected value = (Probability of rolling a 6 * $7) + (Probability of any other outcome * $1)

Since there is only one outcome of rolling a 6, the probability is 1/6 or approximately 0.167. The probability of any other outcome is 5/6 or approximately 0.833. Substituting these values in the formula, we get:

Expected value = (0.167 * $7) + (0.833 * $1) = $1.167

Therefore, the player's expected net winnings for the game is $1.167.