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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?

Verified Answer :

Lizzy190

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: Expected value is -.5 so game not fair

Step-by-step explanation:

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