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:

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

Then the expected value is:

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

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