Question

Compute the extended value on the activities for the school carnival. Does the school make or loose money at each booth? Rolling for dollars!charge: $1 per rollIf you roll…6: you get $55: you get $24: you get $13,2,1: you get nothing

Answer 1

Answer:

Since the expected value of the activity is greater than zero then the school will lose money at each booth.

$EV=\text{ \ }0.33$

Explanation:

Given that on an activity for the school carnival.

Rolling for dollars!

charge: $1 per roll

If you roll…

6: you get $5

5: you get $2

4: you get $1

3,2,1: you get nothing

Computing the Expected value;

$EV=\sum ^{}_{}(\text{ win }\times\text{ Probability)}$

Note: since there is a $1 charge to play, it would be deducted from the win;

$\begin{gathered} EV=\frac{1}{6}(5-1)+\frac{1}{6}(2-1)+\frac{1}{6}(1-1)+\frac{3}{6}(0-1) \\ EV=\frac{1}{6}(4)+\frac{1}{6}(1)+\frac{1}{6}(0)+\frac{3}{6}(-1) \\ EV=\frac{1}{6}(4)+\frac{1}{6}(1)+\frac{1}{6}(0)+\frac{3}{6}(-1) \\ EV=\frac{4}{6}+\frac{1}{6}-\frac{3}{6} \\ EV=\frac{2}{6}=\frac{1}{3} \\ EV=\text{ \ }0.33 \end{gathered}$

Therefore, since the expected value of the activity is greater than zero then the school will lose money at each booth.

$EV=\text{ \ }0.33$