Question

Monty Hall variant. As in the original problem, the car is equally likely to be behind either one of the three doors, numbered #1, #2, and #3. However, after you selected a door, the host opens the other two doors, revealing goats behind them. You now have the opportunity to switch your choice. What is the probability of winning the car if you switch?

Answer 1

In the scenario described, after revealing goats behind both of the other two doors, there is no opportunity to switch to a winning door, making the probability of winning a car by switching 0%.

Step-by-step explanation:

The Monty Hall problem is a famous probability puzzle, and understanding a variant of it requires knowledge of conditional probability and mutually exclusive events.

In the described variant, the host opens two doors to reveal goats after you've made your initial choice. The problem states you now can switch doors, but since both remaining doors are open and show goats, there is no door left to switch to that could potentially have a car behind it.

Thus, the probability of winning the car when offered a switch in this scenario is 0%, as there are no more closed doors to choose from and the car is not behind any of the revealed doors.