Question

In the Monty Hall problem we had three doors, car behind a randomly chosen door, contes-...

In the Monty Hall problem we had three doors, car behind a randomly chosen door, contes-
tant chooses a door with no knowledge of where the car is, host opens a door di erent from the
contestant's choice, but an empty one chosen at random among the available empty, unselected
doors. Then the contestant is asked if she wants to switch her choice to the remaining door.
We saw in class that if the contestant switches, the probability of winning the car was 2/3.
We now add a twist on this problem. Our host really likes the number 3. So if 3 is an available
valid choice, he will de nitely open door 3. Namely, if the contestant does not choose 3 and door 3
is empty, he will de nitely open door number 3 regardless of what other choices are available. Of
course, if 3 is not a valid choice for the door, he continues to choose a door randomly among the
valid choices.
What is the probability our contestant will win the car with the switch strategy?

Math   Statistics-And-Probability   
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