This problem throws many people, even a number of ‘expert’ mathematicians. Suppose you first choose envelope A:
|Round-the-world tickets are in||Host opens||If you stick||If you switch|
|Envelope A||B or C||Star prize||Booby prize|
|Envelope B||C||Booby prize||Star prize|
|Envelope C||B||Booby prize||Star prize|
The star prize is equally likely to be in any of the three envelopes. You therefore have a 2 in 3 chance of winning the round-the-world tickets if you change your mind, compared to a 1 in 3 chance if you stick. Consequently, you are better off opening the envelope you didn’t choose first.