Thanks to the American Mathematical Society, Dartmouth is giving away the much-praised textbook, Introduction to Probability by Charles M. Grinstead and J. Laurie Snell, as free etext. The website also includes computer programs to go along with the book.
Suppose you're on Monty Hall's Let's Make a Deal! You are given the
choice of three doors, behind one door is a car, the others, goats. You
pick a door, say 1, Monty opens another door, say 3, which has a goat.
Monty says to you "Do you want to pick door 2?" Is it to your advantage
to switch your choice of doors?Marilyn [vos Savant] gave a solution concluding that you should switch, and if you do, your
probability of winning is 2/3. Several irate readers, some of whom identified themselves
as having a PhD in mathematics, said that this is absurd since after Monty
has ruled out one door there are only two possible doors and they should still each
have the same probability 1/2 so there is no advantage to switching. Marilyn stuck
to her solution and encouraged her readers to simulate the game and draw their own
conclusions from this. We also encourage the reader to do this (see Exercise 11).
Link (via Interesting People)
Reader comment:
Tim Nicholas says:
Jamie White goes into even greater detail about the "Let's Make a Deal" formula in his book Crimes Against Logic, which I recomend to anyone even marginally interested in logic, probability, and critical thinking. I think it would serve as a nice companion to both this textbook as well as to Daniel Gilbert's SXSW presentation posted a while back.
