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At a County fair there is a spinner game with 12 sectors: 2 red sectors, 2 green sectors, 2 blue sectors, and 6 yellow sectors. If the spinner lands on a red sector, the player wins 2 tokens. If the spinner lands on a green sector, the player wins 2 tokens. If the spinner lands on a blue sector, the player wins 2 tokens. If the spinner lands on a yellow sector, the player loses 3 tokens. 

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

A) County fair games are never fair.


B) The expected value is zero, and the game is fair. So the player will break even for a single spin over time.

C) The expected values is 1/2, and the game is fair. The player will win about 0.55 tokens on a single spin over time.

D) The expected value is -0.5, and the game is not fair. So the player will lose about 0.5 tokens for a single spin over time.

 Dec 20, 2018
 #1
avatar+100516 
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Here's my best attempt, Cupcake.......someone else should verify this....

 

Expected value =

 

Prob of red * payoff + Prob of green * payoff + Prob of blue * payoff + Prob of yellow * payoff  =

 

2/12 ( 2)  + 2/12 ( 2) + 2/12 ( 2) +  6/12 (-3)  =   - 1/2

 

"D"

 

I believe that....to be a fair game, the payoff for the  yellow should only be losing 2 tokens...

 

cool cool cool

 Dec 20, 2018
edited by CPhill  Dec 20, 2018

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