please show work thank you A roulette wheel in the US contai

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A roulette wheel in the U.S. contains 38 equally sized spaces. Two spaces are green, 18 are red and the other 18 are black. The net winnings on a roulette wager can be thought of as a random variable. The payout for betting on red is 1 to 1: if you bet dollar1 on red and red occurs, then you win your dollar back and another dollar. If you bet dollar1 on red and another color occurs, then you lose the dollar that you bet. You have a stack of three chips (S50 denomination each) and you decide to use the following strategy: You will let one chip on red in round 1. Regardless the result you get in round 1, you will bet two chips on red in round 2. If you have at least less than 4 chips by the end of this round, you stop playing. If you have at least 4 chips after round 2, you will bet four chips on red in round 3 and stop playing at the end of this round. Let X be the total amount of money that you have at the end of the game: Find the expected value of X. Find the standard deviation of X (2 marks). What is the probability that you end up with more money than the one you had at the beginning of the game? Explain if this was a fair game for you as a player

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