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Probability Again

Russell Dear

There have been many puzzlists posing probability problems, from Samuel Pepys to Lewis Carroll. One of the most original was Professor Frederick Mosteller, who taught statistics at Harvard University, and who wrote a series of standard texts on probability and statistics. His book Fifty Challenging Problems in Probability (Dover Publications) is a real gem and contains problems which well-known recreational mathematicians Martin Gardner and Ross Honsberger have both expanded into chapters in their various books. Many of his problems, which at first seem disarmingly simple, are quite complicated, but these two are accessible to anyone who is prepared to work carefully through the possibilities.

The Sock Drawer

A drawer contains red socks and black socks. When two socks are drawn at random, the probability that both are red is 1/2.

(a) How small can the number of socks in the drawer be?

(b) If the number of black socks is even, how small can the number of socks in the drawer be?

Successive Wins

To encourage Elmer's promising tennis career, his father offers him a prize if he wins at least two sets in a row in a three-set series to be played with his father and the club champion alternatively, i.e. father-champion-father or champion-father-champion, according to Elmer's choice. The champion is a better player than Elmer's father. Which series should Elmer choose?

Russell Dear is a Mathematician living in Invercargill