Assume that the cost to spin the wheel once is $5.00. and that you will receive the amount shown on the spinner after it stops. The numbers on the wheel are: $5.00 and $10.00 and $0.00. Detetrmine whether the following figure represents a fair game and give the Expectation.

Question

Assume that the cost to spin the wheel once is $5.00. and that you will receive the amount shown on the spinner after it stops.  The numbers on the wheel are: $5.00 and $10.00 and $0.00. Detetrmine whether the following figure represents a fair game and give the Expectation.

anonymous · Answer

expectation is mean right ?

anonymous · Answer

yes that's correct

anonymous · Answer

This is in alegbra and application class on probability. Thank you

anonymous · Answer

welcome. hope it helps

anonymous · Answer

keira- did you reply with answer? I am new to this site and not sure where the answers are displayed, I don't see it if you did.  Thank you

anonymous · Answer

mean = 5. since 15/3 is 5. I dont give the answer because I thought u already get it. Is my answer correct ?

anonymous · Answer

and its not fair game since there is 0.00.

anonymous · Answer

are the areas on the spinner the same?

anonymous · Answer

the expectation without paying the $5 is 
$$\frac{1}{3}\times 0+\frac{1}{3}\times 5+\frac{1}{3}\times 10=\frac{15}{3}=5$$

anonymous · Answer

with paying the $5 the expectation is 0, and therefore it is a fair game, since that is the definition of a fair game, a game with zero expectation

anonymous · Answer

of course i was assuming that each number {0,5,10} shows up with probability 1/3

king · Answer

it is fair as probability of winning is 1/3,losing is 1/3 and neither winning nor losing is 1/3

anonymous · Answer

that is true, but the reason it is fair is that the expected value is 0
if you paid $6 to play this game it would not be fair

anonymous · Answer

Keria- Thanks for your help!