An individual has $$100.$ There is a $25\%$ risk that the individual loses $$90$

are lost. If the individual is careful, the risk of losing the money decreases

to $10\%.$ The cost of being careful is equivalent to $$10.$ The individual's

utility function is $U(x)=\sqrt[\phantom{2}]{x}.$

If the individual takes out insurance, they receive $$50$ in case of loss. The

insurance premium is $$25.$ Which statement is correct?

The individual does not take out insurance regardless of the price of a unit of

insurance.

If insured, the individual is going to be careful.

The individual takes out insurance.

If uninsured, the individual is going to be careful.

None of the answers is correct.