Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
•• A gambler has $100 and makes a series of $1 bets that he can correctly guess the outcome of a coin flip — heads or tails. (The coin and the game are honest, so for every coin flip, there is a 50% chance that the gambler will guess correctly.) The gambler will quit when he has either won an additional $100 or has lost all his money. About how many times will the gambler bet before quitting? [Hint: This situation is like a random walk in one dimension.]
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