Hey everyone, I was given this fun little probability question from my tutor after I finished early in one of my classes about three weeks back, and I just can't seem to crack it!! Something about gambling and probability makes my brain go haywire (or maybe its some other, deeper problem :uhh:). Anyway,here it is, and have fun!! A roulette wheel is numbered from 0 to 36. 0 is Green. Half of numbers are Red and half are Black. The game has an entrance fee $1. The player then stakes $10 and must choose the parity (Odd or Even) and the color (Red or Black). If he gets right parity or color $12 is returned, that is a gain is $1. If he get right both parity and color $20 is returned, , that is a gain is $9. If he does guesses neither correct color nor parity, and the number is not 0, then the entrance fee $1 is returned. If 0 comes up, the player gets nothing. (a) If X is the gain on a single game, complete the table of the probability distribution of random variable X: (b) Find E(X) and standard deviation of X (c) If player plays twice, what is the probability that he comes out ahead (i.e. positive net gain). (d) If player plays this game fifty times, find the mean and standard deviation of his overall net gain. (e) Use your answer to part (d) and a suitable approximation to calculate the probability of coming out ahead after playing fifty games. (f) Given a roulette wheel where the half of odd numbers are Red and half are Black, and similarly for even numbers, check that color and parity appear independently.