A gambling book recommends the following strategy for the game of roulette. It recommends that the gambler bet $1k on red. If red appears (which has probability of 18/38) , then the gambler should take her profit of $1 (in addition to her capital) and quit. If the gambler loses this bet, she should then make a second bet of size $2 and then quit.

a) What is the probability that her winnings from executing this strategy will end with a return for the gambler?

b) What are the expected winnings of the gambler by executing this strategy from the book?