Dave Harris gave a great mathematical explanation but I wanted to give a more intuitive version of what he's saying.
If you assume that the safe option is option A and the risky option is option B then you first need to determine the expected value for each option.
Option A's expected value is
$2,000, meaning no matter what the benefit of option A is
Option B's expected value is
(10000 * .25) + (500 * .75) = 2875.
If the individual was risk neutral they would clearly choose option B because it has a $875 higher expected value than option A.
This individual is risk adverse meaning they put some value on not facing risk or facing less risk. This value that they place on avoiding the risk is referred to as the risk-premium. The value of the risk premium depends on the factors mentioned by Dave Hariss but in essence it is the amount of additional money they most receive to take the risk.
In your example, for the individual to choose the safe option, their risk premium for this situation must be > 875. Otherwise they will choose the risky option despite being risk adverse.