Given two lotteries, L1=(x1,x2;p1,p2) and L2=(x1,x2;q1,q2), and a real number alpha, 0

Given two lotteries, Ll=(x1,x2;p1,p2) and L2=(x1,x2;q1,q2), and a real number alpha, 0 < alpha < 1, show that the result from "mixing" the two lotteries with probabilities alpha and I-alpha is itself a lottery. First draw the diagram associated with the compound lottery in which you receive Ll with probability alpha and L2 with probability I-alpha. Then find the probability with which this compound lottery results in xl and the probability with which it results in Finally, verify that these two probabilities themselves satisfy the definition of a probability distribution (weakly greater than zero and sum to 1).