Question

Some students developed math games for a school carnival. One of the games uses the spinner shown below. The outcomes for the spinner are for a player to win either 1 coupon, 5 coupons, or 10 coupons. It costs a player 3 coupons to turn the spinner once. What is the expected payoff, in coupons, for the game? A. 1/8 coupon B. 5/8 coupon C. 3 1/8 coupons D. 3 5/8 coupons

Answer 1

The expected value is fiven as:

`EV=\sum ^{}_{}x_iP(x_i)`

where xi is the possible outcome and P(xi) is its probability.

From the spinner we notice that:

`\begin{gathered} P(1)=(4)/(8)=(1)/(2) \\ P(5)=(3)/(8) \\ P(10)=(1)/(8) \end{gathered}`

Then the expected value is:

`\begin{gathered} EV=1((4)/(8))+5((3)/(8))+10((1)/(8)) \\ EV=(4)/(8)+(15)/(8)+(10)/(8) \\ EV=(29)/(8) \\ EV=3(5)/(8) \end{gathered}`

Therefore the expected value is 3 5/8 and the answer is D.