AI makes use of probability-based predictive analysis. It is true for generative AI or focused models for specific predictions and pattern recognition. It also holds water in other AI apps, e.g. product recommendations to prospective buyers.

Let us consider here the probability puzzle called the Monty Hall Problem. Here the host of a popular game show Let’s Make a Deal presents before the contestants three doors. There is a car behind one door, and there are goats behind the other two doors. The host knows what is behind each door. The contestant is asked to pick up a door. The host then opens up one of the remaining two doors to reveal a goat. The contestant can stick to his original choice of door or can switch the option to other unopened door. What should he do?

To begin with, out of the remaining two doors, it is considered to be a case of 50 per cent probability of winning the car, irrespective of whether the contestant sticks to the original door or switches the door. Mathematically, however, the chances of winning are doubled if there is a switch of decision. The host has removed one of the losing doors. He has left two doors, with one having a car behind. If the contestant switches a choice, the contestant has bet his initial choice wrongly and the car is behind the remaining unopened door.

In other words, if the initial choice was door one, there was equal probability across the three doors or one third chance. One door was opened, say door three. Thus its probability has become zero, Door two has now a probability of 2/3, since the probability of the third door gets added to it. This is counterintuitive reasoning.

This problem highlights the importance of understanding probabilities and their limitations in decision making. It applies to the application of AI.