Business Analytic: A Probabilistic Decision-Making

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Business Analytic: A Probabilistic Decision-Making

The famous Monty Hall problem involved the following situation: the contestants appeared to have a perfectly basic choice in choosing one out of three doors that would lead to a car. Of course, a goat was shown behind one of the doors, and the contestants had to switch doors as though they needed to decide.

At first look, when there are only two doors left and the situation becomes a 50-50 chance, there is no difference between switching and keeping. But this intuition needs to be corrected. That probability becomes twice as much if the candidate switches doors and one of the doors opens to a goat. Here’s why:

When the contestant first chooses a door, there is a 1/3 probability that the car is behind that door; hence, the likelihood that the car is behind one of the other two doors is 2/3. As the door revealing the car was chosen among the original three, the 2/3 chance now goes to the unopened door. According to Johansen (2021), the probability of selecting the car increases by switching from 1/3 to 2/3. My immediate gut reaction is to stay with the original choice.

This is based on some form of emotional attachment or a feeling that the odds must be evened up somehow, but knowing the nature of the problem’s probability; I would change the doors. I would pick door No. 2. That follows logically by probability; hence, I maximize my chances for the car. It may seem counterintuitive, but the math following the decision shows an increased likelihood of a more data-centered approach, even with something random like a game show.

References

Johansen, L. M. (2021, November 22). Quantum theory is logically inevitable. ArXiv.org. https://doi.org/10.48550/arXiv.2111.05619