11 (The Allais Paradox) Suppose we are offered a choice between the following two lotteries:

L1: With probability 1, we receive $1 million.

L2: With probability .10, we receive $5 million.

L2: With probability .89, we receive $1 million.

L2: With probability .01, we receive $0.

Which lottery do we prefer? Now consider the following two lotteries:

L3: With probability .11, we receive $1 million.
L2: With probability .89, we receive $0.
L4: With probability .10, we receive $5 million.
L2: With probability .90, we receive $0.
Which lottery do we prefer? Suppose (like most people), we prefer L1 to L2. Show that L3 must have a larger expected utility than L4.