Take Your Pick

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.