Brain Teaser: Probability and Statistics

I will stick with my choice if I am on the game show and select door #1, and the host opens door #3 to reveal a goat behind it. This is because opening the third door only supports my intuition that I might have selected the correct option. The car is behind one of the remaining doors, and changing my choice will not significantly affect the result. However, probability and statistics show that this is not the case and the odds have significantly shifted to one door.

In the context of this teaser, probability and statistics teach how to determine the chances of the car being behind one of the two remaining doors. The idea is to calculate the probability associated with each option by considering their number. In this case, there was a 33.3% chance of selecting the right door. However, upon opening the third door, the probability of choosing where the car was located shot up to 50%. This would be the case if the host did not know the car’s location, but they do. This means now each door has unequal potential, so switching is to the player’s benefit (Feliciano-Semidei et al., 2022). For this reason, I would switch to door #2 because the car is probably behind it.

So many people may get upset at this brain teaser because they do not understand probability and statistics. Once the third door opens and reveals the goat, many people need to realize that the odds are unequal because the host knows where the car is. Instead, they think the odds are still the same, which is not the case. Therefore, they get frustrated by the problem they face because they believe each option has the same odd of yielding a positive result. In reality, the host’s knowledge has changed the odds in this game of chance.

Reference

Feliciano-Semidei, R., Wu, K., & Chaphalkar, R. M. (2022). Introducing conditional probability using the Monty Hall problem. Journal of University Teaching & Learning Practice, 19(2), 93-109. Web.

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