A game is played using one die. There is a$1 charge to play the game. If the die is rolled and shows a five, the player receives $6 back ( a profit of $5 and the original $1). If any other number shows, theplayer loses the original $1. What is the player's expected value? - did not match any documents. No pages were found containing "A game is played using one die. There is a$1 charge to play the game. If the die is rolled and shows a five, the player receives $6 back ( a profit of $5 and the original $1). If any other number shows, theplayer loses the original $1. What is the player's expected value?".

Investing is a game of chance of making a single free throw. Assume that free throw shots are independent of one another. Suppose this player get to shoot four free throws find the probability that he misses all four consecutive free throws. Round to the nearest ten- thousandth

To find the player's expected value, we need to calculate the average amount of money the player can expect to win or lose per game.

Step 1: Determine the probabilities of each outcome.
Since the die has six sides and only one side shows a five, the probability of rolling a five is 1/6. The probability of rolling any other number is 5/6.

Step 2: Calculate the expected value.
Multiply the probabilities of each outcome by their respective amounts and sum them up.

For rolling a five:
Probability of rolling a five = 1/6
Amount won (profit) = $5
Expected value for rolling a five = (1/6) * $5 = $5/6

For rolling any other number:
Probability of rolling any other number = 5/6
Amount lost = $1
Expected value for rolling any other number = (5/6) * (-$1) = - $5/6

Now, add up the two expected values:
Expected value = $5/6 - $5/6 = $0

Therefore, the player's expected value is $0. This means that, on average, the player neither wins nor loses money in the long run.

To find the player's expected value, we can calculate the average outcome by multiplying each possible outcome by its probability and summing them up.

In this game, there are two possible outcomes:
1. Rolling a five: The player receives $6 back (profit of $5 + the original $1). Since there is only one "five" on a standard die, the probability of rolling a five is 1/6.
2. Rolling any other number: The player loses the original $1. Since there are five numbers (1, 2, 3, 4, 6) that are not a five, the probability of rolling any other number is 5/6.

Now, let's calculate the expected value:

Expected value = (Probability of outcome 1 * Outcome value 1) + (Probability of outcome 2 * Outcome value 2)

Expected value = (1/6 * $6) + (5/6 * (-$1))

Expected value = $1 - $0.83

Expected value ≈ $0.17

Therefore, the player's expected value is approximately $0.17.