Your wealth contains 10$ and 2 items: Item 1 is worth 10$ while item 2 is worth 20$. The probability for item 1 to be lost is 10% and the probability for item 2 to be lost is also 10%. Therefore, you would like to purchase an insurance against these possibilities. Your utility function is defined by u (x) = ln x and you are expected to be a utility maximizer. Compute in each case the maximum premium you want to pay for getting a full insurance (this means that you are fully compensated if you lose one or two items).

a) Both events "Item 1 is lost" and "Item 2 is lost" are unrelated random events.

b) The two events are perfectly correlated.