Is the last envelope the richest?

Question

Ten envelopes each contain an independent random amount of money, all drawn from the same continuous distribution, so no two amounts match. You open them in some fixed order.

What is the probability that the last envelope you open holds the largest amount?

Accepted Answer

The order in which you open the envelopes has no effect on which one happens to hold the most money. All ten amounts are exchangeable, so each envelope is equally likely to be the biggest. The last one is one of ten equally likely holders: \frac{1}{10} = 0.1. Takeaway. Opening order never changes an extreme's location; any labeled item is the maximum with probability 1/n.

Is the last envelope the richest?

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