1. ## Expected value

Tom and Savoy decide to play the following game for points. A single die is rolled. If it shows a non-prime, Tom receives points equal to twice the number of dots showing. If it shows a prime, Tom loses points equal to 3 times the number of dots showing, What is the expected value of the game?

I'm very confused by expected value and when this word problem was given it totally threw me off. Can you please help me? Just give me a helpful hint-not the answer.

Thank you very much!

2. To solve an expected value question, you need this formula,

$\displaystyle E(X)=\Sigma{xP(x)}$

Construct a table like this

xPoints gained/lost): 2 4 6...
P(x): Probability $\displaystyle \frac{1}{6}$ $\displaystyle \frac{1}{6}$ $\displaystyle \frac{1}{6}$....
Multiply each x by its corresponding P(x) and then find the sum of these values and you will have found th expected value.

3. Hello, acharles!

Tom and Savoy decide to play the following game for points.
A single die is rolled.
If it shows a non-prime, Tom receives points equal to twice the number of dots showing.
If it shows a prime, Tom loses points equal to 3 times the number of dots showing.
What is the expected value of the game for Tom?
There are only six outcomes . . . make a chart.

. . $\displaystyle \begin{array}{|c||c|c|} \hline \text{Outcome} & \text{Payoff} & \text{Prob.} \\ \hline \hline 1 & +2 & \frac{1}{6} \\ \\[-4mm] 2 & -6 & \frac{1}{6} \\ \\[-4mm] 3 & -9 & \frac{1}{6} \\ \\[-4mm] 4 & +8 & \frac{1}{6} \\ \\[-4mm]5 & -15 & \frac{1}{6} \\ \\[-4mm] 6 & +12 & \frac{1}{6} \\ \hline \end{array}$

Got it?