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.

Mr F asks: What does this mean? Do you mean on the next spin, the next two spins, .....??
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?

Mr F says: It's one way of doing it, I suppose. But it would help to know the answer to my above question.
(b) What is the definition of a winning strategy?

Mr F says: E[X] > 0.
(c)

Mr F asks: And your question is ....?