(3b) Consider the Monty Hall problem discussed in lecture. Take the case where there are 6 doors. Behind 5 doors there are goats and behind 1 door there is a car. You will pick a door and then the host will open 4 remaining doors revealing goats. Assume that you always then switch to the last remaining door. What is the probability of winning the car?
(3b) Consider the Monty Hall problem discussed in lecture. Take the case where there are 6 doors. Behind 5 doors there are goats and behind 1 door there is a car. You will pick a door and then the host will open 4 remaining doors revealing goats. Assume that you always then switch to the last remaining door. What is the probability of winning the car?
(3c) At a casino a game of roulette is being played. In each round of this game a ball is dropped. The ball can land on either a black square or a red square (with equal probability). What is the probability of observing that the ball land on black, 16 times in a row?
(3d) Consider the same roulette game as the previous question and you have observed black come up 16 times in a row. For the next bet, your friend tells you that you should definitely bet on red because the likelihood of getting black again is extremely low based on the past observation. Explain in 3-4 sentences if your friends logic is correct?
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