For this task we\'ll investigate a famous problem in probability: the Monty Hall

Question

For this task we'll investigate a famous problem in probability: the Monty Hall Problem. It's based on a game played in the TV game-show Let's Make a Deal, which was hosted by a man named Monty Hall. Here is a description of the problem: There are 3 doors, numbered 1, 2, and 3. Behind one door is a great prize, and behind the other two doors are “dud" prizes. The contestant chooses a door Monty Hall opens one of the doors they did not choose, and he always opens a door that reveals a dud prize. The contestant then has the option to stick with their initial choice of door, or change to the other remaining unopened door. The door finally chosen by the contestant is then opened to reveal either the great prize or the other dud prize. 1. 2. 3. 4. a) Consider the random process in which the prizes are assigned to doors. The three possible outcomes of this random process are: D1: The great prize is behind door 1 D2: The great prize is behind door2 D3: The great prize is behind door 3 Assuming the prize assignment occurs completely at random, write down the probability model that corresponds to this process (Hint: this means you'll need a table that lists all the possible outcomes and the probability of each outcome) b) b) The question we'll nvestigate relates to step 3 above: is t better for the contestant The question we'll investigate relates to step 3 above: is it better for the contestant to stick with their initial choice, to switch to the other unopened door, or are the chances of winning the same either way? Suppose your strategy is to always choose door 1 and stick with it. What is the probability of winning the great prize? Write down your answer using statistical notation and reasoning

Explanation / Answer

a) If the prize is behind D3

Event Probability of winnig Opening of D1 1/3 Opening of D2 1/3 Opening of D3 1/3

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