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4. This questions is adopted from the Martingale doubling system question in Homework 1. In roulette, the probability of red is Iii/'38. Suppose you bet on red and use the Martingale doubling system: every time you win, bet $1 next time; every time you lose. double your previous bet. Suppose you play this game until you have won more than $20 or you have lost more than $50. Use simulation to answer the following questions. [1) What is the probability that you end up winning more than $20 at the end"? [2) On average1 how many games will you be playing? (3) Estimate the distribution of the game length by plotting a histogram