There are four different monetary prizes in separate sealed envelopes, and you want to pick the biggest prize. You can pick an envelope, open it, and take the prize in that envelope. Or, you can reject that prize and pick a second envelope. However, if you do that, you cannot go back and take the prize in the first envelope you selected. Or, you can reject the prizes in the first two envelopes you select, and pick a third envelope. However, if you do that, you cannot go back and take either of the prizes in the first two envelopes that you selected. In other words, once you reject a prize, you cannot go back and reclaim it.

a. What is the rule (strategy) you should choose to maximize the probability that you get the biggest prize? That is, what is the optimal decision rule to get the biggest prize?

b. What is the probability that you get the biggest prize when using the optimal rule?