Question

7. The Price is Right designs a new game for contestants. The game involves spinning a fair wheel with ten segments displaying the numbers 1 to 10. If the spinner lands on an even number you loose the points equal to twice the value of the number. If the spinner lands on an odd number you gain the points to three times the number.

a) What is the expected value of the points received?
b) Is this a fair game? Why or why not?

Answer 1

@jim_thompson5910

Answer 2

a)

E(X) = Sum(probability*value)


E(X) = (1/10)*(3) + (1/10)*(-4) + (1/10)*(9) + (1/10)*(-8) + (1/10)*(15) + (1/10)*(-12) + (1/10)*(21) + (1/10)*(-16) + (1/10)*(27) + (1/10)*(-20)


E(X) = 0.3 - 0.4 + 0.9 - 0.8 + 1.5 - 1.2 + 2.1 - 1.6 + 2.7 - 2


E(X) = 1.5


So the expected value is 1.5 points. In other words, you expect to win 1.5 points on average each spin.


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b)

The game is not fair since the expected value is not zero.

Answer 3

Note: just because the game isn't "fair", it doesn't automatically mean it's bad for the player (it's unfair because the owner loses points over the long run)

Answer 4

Thank you! :D

Answer 5

sure thing