Financial Modeling Self Study Program

Three envelopes are presented in front of you by an interviewer. One contains a job offer, the other two contain rejection letters. You pick one of the envelopes. The interviewer then shows you the contents of one of the other envelopes, which is a rejection letter. The interviewer now gives you the opportunity to switch envelope choices. Should you switch?

The answer is yes.  Say your original pick was envelope A.  Originally, you had a 1/3 chance that envelope A contained the offer letter.  There was a 2/3 chance that the offer letter was either in envelope B or C.  If you stick with envelope A, you still have the same 1/3 chance.  Now, the interviewer eliminated one of the envelopes (say, envelope B), which contained a rejection letter.  So, by switching to envelope C, you now have a 2/3 chance of getting the offer and you’ve doubled your chances.

Note that you will often get this same question but referring to playing cards (as in 3-Card Monte) or doors (as in Monte Hall/Let’s Make a Deal) instead of envelopes.

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