Alan's current income is $$100,000.$ Alan believes that he owes $$20,000$ in taxes. For $$500,$ he can hire a CPA to review my tax return; there is a $20\%$ chance that she will save him $$4,000$ in taxes. His utility function for $($disposable income$)=($current income$)-($taxes$)-($payment to accountant$)$ is given by $\sqrt[\phantom{2}]{x}$ where $x$ is disposable income. Should he hire the CPA?