In the casino game of Roulette, there are 38 slots on the wheel. Of the 38 slots, 18 are colored red, 18 are colored black, and 2 are colored green. For a single game, the wheel is spun and a ball is rolled. Eventually, the ball will randomly fall into one of the slots. For the next game, the wheel is respun and the ball rerolled, making the outcome independent of the previous outcome.(a) On a single game, what is the probability that the outcome is red? P(red) = 18/38 = 0.474.(b) Suppose a casino patron plays the game 20 consecutive times and bets that the outcome will be red each time. What is the probability that the patron is correct (and wins) on exactly 10 of the games?(c) Suppose a casino patron plays the game 20 consecutive times and bets that the outcome will be red each time. What is the probability that the patron is correct (and wins) on at most 10 of the games?(d) Suppose a casino patron plays the game 20 consecutive times and bets that the outcome will be red each time. What is the probability that the patron is correct (and wins) on at least 15 of the games?
