Suppose that over the course of several days a gambler makes

Suppose that, over the course of several days, a gambler makes 3300 row bets in roulette, betting SI each time. For a row bet, the gambler selects a row of 3 spaces out of the 38 possible spaces on a roulette table. If the gambler wins on one play, the gambler get his/her dollar back plus eleven more, for a net gain of $11. However, if the gambler loses, he/she loses $1. Find the probability that, after making these 3300 row bets, that the gambler wins at least $0. (Round your answers to four decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.

Solution

probability of winning is 1/38

so in 3300 bets according to the probability of 1/38

he would have won 3300*1/38 = 87 bets

and each wining bet gives him 11 dollar

therefore 87*11 =957 bets

for 3300 bets, he spend 3300 dollar

so he lost 3300-957 = 2343

so probability of winning at least 0 = 857/3300 = 0.259