Calculating Expected Value for Sweepstakes Prizes

[layzieb81]

The prizes that can be won in a sweepstakes are listed below together with the chances of winning each one.

$5900(1 chance in 8100); $2500( 1 chance in 6200); $600 (1 chance in 4700); $300(1 chance in 2600)
Find the expected value of the amount won for one entry if the cost to enter is
75 cents.

Now I am having trouble setting this up as a probability distribution. I just don't know where to start or what goes where. I know the awnser is $0.62..but i just can't figure out the steps. So far i'v been doing it like this

x P(x)
----- ------
Win $5899.25 ?
Lose -$.75 ?

Well I think I'm setting up "x" wrong and I just don't know what the probability should be. So any help would be apreciated.

 

[Zaare]

For example, 1 chance in 100 is a probability.
So you have the probability of every winning and the amount of each winning. Now, the expected value is

$$E\left[ X \right] = \sum\limits_{i = 1}^n {X_i P\left( {X_i } \right)}$$

$$X_i$$ is the amount of each winning and $$P\left( {X_i } \right)$$ is the probability of each winning.
And don't forget to take into account the 75 cents the entry consts.

 

[HallsofIvy]

"One chance in 8100" means the probability is 1/8100, "one change in 6200" mean the probability is 1/6200, etc.