SOLUTION: At a carnival game you pay $3 for a ticket to spin the wheel and win the amount shown. The odds are listed below: 25% chance win $0 25% chance win $2 50% chance win $5 1.C

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Question 981077: At a carnival game you pay $3 for a ticket to spin the wheel and win the amount shown. The odds are listed below:
25% chance win $0
25% chance win $2
50% chance win $5
1.Calculate the expected value for this game according to these directions:
a).Multiply the probability of the event occurring times the payoff for that event.
b).Repeat step 1 for all possible events
c).Sum up all the results from steps 1 and 2
2.Is this a fair game? (Does the amount you pay = what you expect to win)
I am completely lost on this one. Any help is greatly appreciated!

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
1)

Factoring in the cost to play the game ($3)

If you win $0, then you really gain -3 dollars (ie you lost $3)
If you win $2, then you really gain -1 dollars (ie you lost $1)
If you win $5, then you really gain 2 dollars (you finally have won some money)

Probability Net Gain
0.25 -3
0.25 -1
0.50 2

Multiply the probabilities with their corresponding net gain

0.25*(-3) = -0.75
0.25*(-1) = -0.25
0.50*(2) = 1

Add up those results

-0.75+(-0.25)+1 = 0

The expected value is 0.

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2)

From problem 1 above, we found the expected value to be 0. This is a fair game because, over the long run, you gain on average $0. You neither win money nor lose money. The same applies to the person running the game. Both sides (you and the person running the game) are equal.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
At a carnival game you pay $3 for a ticket to spin the wheel and win the amount shown. The odds are listed below:
25% chance win $0
25% chance win $2
50% chance win $5
1.Calculate the expected value for this game according to these directions:
a).Multiply the probability of the event occurring times the payoff for that event.
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0.25*0 + 0.25*2 + 0.50*5 = 3.00
b).Repeat step 1 for all possible events
done above
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c).Sum up all the results from steps 1 and 2
done above
2.Is this a fair game? (Does the amount you pay = what you expect to win)
Ans: Yes it is fair. Expected win = cost to play.
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Cheers,
Stan H.
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