Consider the following two investment opportunities for a venture capital firm: Opportunity Y has a success probability of 10%. If it is successful, it will be worth $10M; otherwise it is worth $0. Opportunity Z has a success probability of 50%. If it is successful, it will be worth $2M; otherwise it is worth $0. (The expected payoff to each of the two opportunities is the same$1M). The Limited Partners investment is $0.8 M (the General Partner does not put in any money). The contract calls for the GP to make 20% in carried interest with no fee. Assume risk neutrality and no discounting: a. Which opportunity would the GP prefer? Why? b. Which opportunity would the LP prefer? Why? c. Why (under what conditions) might the LPs like this carried interest compensation contract in spite of the apparent conflict in incentives?