Ask Marilyn ® by Marilyn vos Savant is a column in Parade Magazine, published by PARADE, 711 Third Avenue, New York, NY 10017, USA. According to Parade, Marilyn vos Savant is listed in the "Guinness Book of World Records Hall of Fame" for "Highest IQ."
In her Parade Magazine column of March 31, 1996, Marilyn claimed that the chances of reaching into a closet without looking, pulling out a shoe with each hand, and coming up with a matching pair of shoes from among two pair of shoes in the closet is only 1/3.
Think outside the lines Marilyn: These are not two pair of equally shaped items. These are shoes. The only constraint is that you reach in without "looking." If you use your sense of touch when grabbing the shoes you could be assured of getting a left and right shoe, thus improving the odds to 1 out of 2.
Park Chamberlain <firstname.lastname@example.org> writes:
Think outside the lines some more. In the real world it's very unlikely that both pairs would be identical to the touch. You could feel around until you were pretty sure you had a left and a right from the same pair, thus improving your odds to 90% or better.
Of course, most people tend to sort their shoes. If you always picked two shoes that were next to each other, that would improve your odds too.
Why do these answers seem wrong? It's because they violate the unwritten assumptions of the problem that the pairs are identical and the shoes are stored, and therefore retrieved, randomly.
Most if not all word problems rely on the reader's understanding and accepting such unwritten assumptions. Some people hate word problems--part of the reason may be that they never pick up on this fact.