Suppose Sam is risk averse with a utility of wealth function given by u(w)=w . Sam invests all she owns in a savings account promising to pay 400 euros with probability p and 900 euros with probability (1-p). She also had the option of investing in a plan which guaranteed a payment of 576 euros.

(i) what values of p are consistent with Ann choosing the riskier plan? Please show the equation used and the math's derivations.