Probability Distribution Question

Hi

Im having this problem with a Probability Distribution question.. I just don't seem to know how to do this.

So here's the question:

**A spinner with five regions is used in a game. The probabilities of the regions are...**

P(1) = 0.3

P(2) = 0.2

P(3) = 0.1

P(4) = 0.1

P(5) = 0.3

The rules of the game are as follows: If you spin and land on an even number, you receive double that number of points. If you land on an odd number, you lose that number of points. What is the expected number of points a player will win or lose.

I did find the expected number and my answer was right.. but then question e) confused me...

e) alter the game to make it fair. Prove mathematically that your version is fair.

In the other questions i had to do probability distributions and stuff and for the expected value i got a number other than 0 (basically its an unfair game). But I am really confused as how to alter this game so that the expected number is zero and it is fair.

Thanks in advance