Question

Consider the following game of chance based on the spinner below: Each spin costs $3. If the spinner lands on A the player wins $8, if the spinner stops on D the player wins a penny otherwise the player wins nothing. Calculate the players expected winnings. Express your answer to at least three decimal places in dollar form. . Answer: $

Answer 1

$2.0025

Explanation:

To calculate the player's expected winnings, we need to multiply each outcome by its probability and sum the results.

The spinner has four equally likely outcomes (A, B, C, and D), so each outcome has a probability of 1/4.

The player wins $8 if the spinner lands on A, which has probability 1/4. So the contribution to the expected winnings from this outcome is:

(1/4) * $8 = $2

The player wins a penny if the spinner lands on D, which also has probability 1/4. So the contribution to the expected winnings from this outcome is:

(1/4) * $0.01 = $0.0025

The player wins nothing if the spinner lands on B or C, each of which has probability 1/4. So the contribution to the expected winnings from these outcomes is:

(1/4) * $0 + (1/4) * $0 = $0

Now we can sum the contributions from each outcome to get the player's expected winnings:

$2 + $0.0025 + $0 = $2.0025

Therefore, the player's expected winnings are $2.0025.

Hopefully this helps!