Question

a game is called fair if its expected value is zero. suppose you are playing this spinner game with a friend: you spin and if it lands on red, your friend gives you $12, otherwise you give your friend $4. is this a fair game?

Answer 1

A game is fair if its expected value is zero. To determine if the spinner game is fair, calculate the weighted average of the outcomes based on their probabilities. The game is fair if this expected value is zero.

Step-by-step explanation:

A game is considered fair if the expected value of the game is zero, meaning that over time, you would neither gain nor lose money on average. To determine if the game mentioned is fair, one must calculate the expected value. Using the given probabilities (though incomplete in the question, let's assume we have the probabilities of landing on red, blue, and green), we calculate:

• The expected gain/loss when the outcome is red.
• The expected gain/loss when the outcome is blue.
• The expected gain/loss when the outcome is green.

Then we add these values to find the overall expected value of the game. If the expected value is zero, the game is fair. If it is positive, it is in favor of the player; if negative, it is in favor of the house.

For the game described with the spinner (red: receive $12, otherwise: pay $4), you would calculate the expected value as follows:

Expected value = P(red) × Gain when red + P(not red) × Loss when not red

If this calculation results in an expected value of zero, then the game is indeed fair.