can someone please help me understand this problem? I dont know how to begin!

Roulette is one ofthe most common games played in gambling casinos in Las Vegas and elsewhere. An American raulette wheel has slots marked with the numbers from 1 to 36 as well as 0 and 00 (the latter is called "double zero"), Half Of the SIDS marked 1 to 36 are colored (ed and the other half are black. (The 0 and 00 are colored green.) With each spin of the wheel, the ball lands in one of these 38 slots One of the many possible roulette hes is to bet on the color of the slot that the ball will land on (red or black). If a player has on red, he wins if the outcome is one or the 15 red outcomes, and he loses if the outcome is one of the 18 black outcomes or is 0 or 00. So, when betting on red, there are 18 outcomes In which the player wins and 20 outcomes in which the player loses. Therefore, when betting on red, the prohlblllty at winning is 18/38 and the probability 0' losing is 20/38. When betting on red, the payout for a win is "1 to 1". This means that the player gets their original bet back PLUS and additional amount equaling their bet. in other words, they double their money. (Note: It the player loses they lose whatever amount of money they bet.) ' e goes to the casino with $409. His plan is to bet $100 on red 9 consecutive times or until he either has increased his total to $500 or has lost all at his money. what is the probability he will go bankrupt (Le. end up with 50)? (Give your answer correct to four decimal places.) (Hint: set this problem up as an absorbing Markov chain with 6 states where the states keep track of his current amount of money. The amount of money he has will always be so, 5100, $200, $300, $400, or ssuo. The states where he has so or 3500 are absorbing states since he quits playing whenever one (If these states is reached. Scenario 1: Mike goes to the casino with $400 and will still be betting on red. As in Scenario 1, he will bet $100 each time he places a bet. However, instead of limiting himself ta a maximum of 9 bes he decides to play indenitely until he has reached $500 or goes bankrupt. If he uses this betting method, what is the probability he will eventually go bankrupt? (lee your answer correct to four decimal places.)