Suppose that Sarah is an Expected Utility Decision maker and her utility over outcomes/wealth z (measured in million ) is given by u(z)= 100* z/z+1. Sarah is a house-owner which is worth w and knows that with probability 1/2 her house is damaged reducing the value to m, such that 0 < m < w while with 1/2 probability no damage will occur. Additionally she has an amount of v on her bank account.

(a) Write down the lottery, its expected value and the expected utility for this lottery over wealth for general v, w, m.