Question

At a county fair there is a spinner game with 10 sectors: 2 red sectors, 2 green sectors, 3 blue sectors, and 3 yellow sectors. If the spinner lands on a red sector, the player wins 3 tokens. If the spinner lands on a green sector, the player wins 5 tokens. If the spinner lands on any other sector, the player loses 2 tokens.

Is this game fair for the player and how much will the player win or lose on an average over time?

Answer 1

Let the token profit be X. For a win, the profit is 2 tokens. For a loss, the profit is -3 tokens. The probability of a win is 212+212+212=612=12 the probability of a loss is 612=12 Setting up a probability distribution variable gives: E(X)=(−3×12)+(2×12)=−112+1=−12 token Therefore, on average, the player would expect to lose a half a token per game.

Answer 2

Answer: Expected value is -.5 so game not fair

Step-by-step explanation: