Uncertainty in an unfair gamble If a risk averse person is given the option of a certain amount of 2000 or playing a lottery game giving him 10000 with 25% probability, and 500 with 75%, then what would he do ?.

The bet here is not a fair one, so wouldn't his choice depend on the degree of his risk aversion ?. Can somebody please help me out.
So let's decided that decision A is taking the certain sum and decision B is taking the risky sum, where $\bar{w}$ is current wealth and $\mathcal{U}$ is a utility function where $\mathcal{U}'&gt;0$ and $\mathcal{U}''&lt;0$, then you have two potential outcomes in utility.  The first is $$\mathcal{U}(A)=\mathcal{U}(\bar{w}+2000)$$ and the second is $$\mathcal{U}(B)=\frac{\mathcal{U}(\bar{w}+10000)+3\mathcal{U}(\bar{w}+500)}{4}.$$

Given only this information, the decision depends upon $\bar{w}$, the shape of $\mathcal{U}$, the payoff outcomes, and the probabilities involved.  If you wanted to determine how sensitive a decision would be to change, you could treat the currently fixed factors as variable factors one at a time.  To provide an example, you could create a new variable $\pi$ so that option A would become $$\mathcal{U}(\bar{w}+\pi).$$

You could also do this to substitute for $\bar{w}$, the other payoffs, or the odds.  If you added the assumption that the actors were indifferent, then you could also use the Envelope Theorem to look at local sensitivity.