Expected Value, given outcomes and their probabilities

Ok, here is my actual question---and I thought I had it but I ust be missing a step. I know the correct answer and am trying to figure out the step I missed to get the final response.

Question:
From the data given, compute the expected value of the outcome.

Outcome: -2000,0,1000,2000
Probability:1/4,1/6,1/4,1/3

I already have -2000(1/4)+0(1/6)+1000(1/4)+3000(1/3) but the number is too outrageous for this problem. I know I am missing a step to make it a small fraction.

Please help out if you can.

Thanks,

Danny

Divide it by 5 to get the average?

why do you say you should get a small fraction

its the expected value of the outcome

the range of the outcome is -2000 to 2000, so you would expect to get a number in that range

Hello, Danny!

I know the correct answer.

From the data given, compute the expected value of the outcome.

. . \(\displaystyle \begin{array}{ccccc}\text{Outcome} & -2000 & 0 & 1000 & 2000 \\
\text{Probability} & \frac{1}{4} & \frac{1}{6} & \frac{1}{4} & \frac{1}{3} \end{array}\)

I already have: \(\displaystyle \:-2000\left(\frac{1}{4}\right)\,+\,0\left(\frac{1}{6}\right)\,+\,1000\left(\frac{1}{4}\right)\,+\,2000\left(\frac{1}{3}\right)\)

but the number is too outrageous for this problem. . Why?

Click to expand...

If this is a gambling game and the payments are in thousands of dollars,
. . why shouldn't the expected value be thousands (or hundreds) of dollars?