A gambling book recommends the following winning strategy for the game of roulette. It recommends that the gambler bets on red. If red appears (which has probability ), then the gambler should take her profit and quit. If the gamblers loses the bet (which has probability of occurring), she should make additional bets on red on each of the next new spins of the roulette wheel and then quit. Let denote the gambler's winnings when she quits.
(a) Find .
(b) Is this a winning strategy?
(c) Find .
For (a) . This is the easy way to compute it?
(b) What is the definition of a winning strategy?