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

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

`EV=\text{ \$}0.33`

Step-by-step 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 }*\text{ Probability)}`

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

`\begin{gathered} EV=(1)/(6)(5-1)+(1)/(6)(2-1)+(1)/(6)(1-1)+(3)/(6)(0-1) \\ EV=(1)/(6)(4)+(1)/(6)(1)+(1)/(6)(0)+(3)/(6)(-1) \\ EV=(1)/(6)(4)+(1)/(6)(1)+(1)/(6)(0)+(3)/(6)(-1) \\ EV=(4)/(6)+(1)/(6)-(3)/(6) \\ EV=(2)/(6)=(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`