Let us consider a variant of the 4Door Deal Problem If the c

Let us consider a variant of the 4-Door Deal Problem. If the contestant chooses the door with the car behind it, then with probability 0.8, the host opens a different door (with no car behind it, of course). If the contestant chooses a door with no car behind it, then with probability 0.9, the host opens a different door with no car behind it. If the host does not open a door, then the contestant gets what he or she originally chose.

What is the probability that Stu wins?

If Monty opens a door, what is the probability that Stu wins?

If Monty opens a door, what is the probability that Zelda wins?

What is the probability that Zelda wins?

Solution

What is the probability that Stu wins?

Probability = 0.8^4 = 0.4096

If Monty opens a door, what is the probability that Stu wins?

Probability = 0.8^4 / 0.9 = 0.4551

If Monty opens a door, what is the probability that Zelda wins?

Probability = 0.8^3 / 0.9 = 0.5689

What is the probability that Zelda wins?

Probability = 0.9^4 = 0.6561