Consider a risk-averse individual with a utility of wealth function U(w) = w^0.5 and initial wealth w = $500. He can invest all his wealth in a safe asset. The asset provides a guaranteed return r = 10% . He can also invest all his wealth in a risky Gamble with a potential capital gain of 60% of the asset's value and a potential capital loss of 30% of the asset's value.

The probability of a capital gain is 65% and the probability of a capital loss is 35%.