1. Consider playing the following modified Monty Hall games: Monty Hall chooses the door behind which he will put the car with probabilities 0.2, 0.1, and p, respectively. That is, the door with the smallest probability to have the car is Door 2. Describe below your strategy in playing this game.
2. (a) First, what is the value of p?
3. (b) Step 1: Which door would you choose at first?
4. (c) Step 2: Would you switch to the other unopened door?
5. (d) What is the probability of winning the car under this strategy? Explain.