# Question: A gambling book recommends the following winning strategy for the

A gambling book recommends the following “winning strategy” for the game of roulette: Bet $1 on red. If red appears (which has probability 18/38), then take the $1 profit and quit. If red does not appear and you lose this bet (which has probability 20/38 of occurring), make additional $1 bets on red on each of the next two spins of the roulette wheel and then quit. Let X denote your winnings when you quit.

(a) Find P{X > 0}.

(b) Are you convinced that the strategy is indeed a “winning” strategy? Explain your answer!

(c) Find E[X].

(a) Find P{X > 0}.

(b) Are you convinced that the strategy is indeed a “winning” strategy? Explain your answer!

(c) Find E[X].

## Answer to relevant Questions

Four buses carrying 148 students from the same school arrive at a football stadium. The buses carry, respectively, 40, 33, 25, and 50 students. One of the students is randomly selected. Let X denote the number of students ...There are two possible causes for a breakdown of a machine. To check the first possibility would cost C1 dollars, and, if that were the cause of the breakdown, the trouble could be repaired at a cost of R1 dollars. ...If E[X] = 1 and Var(X) = 5, find (a) E[(2 + X)2]; (b) Var(4 + 3X). Suppose that a biased coin that lands on heads with probability p is flipped 10 times. Given that a total of 6 heads results, find the conditional probability that the first 3 outcomes are (a) h, t, t (meaning that the first ...Consider n independent trials, each of which results in one of the outcomes 1, . . . , k with respective probabilities Show that if all the pi are small, then the probability that no trial outcome occurs more than once is ...Post your question