Perils of Probability

Bill Lee

Probability rules our lives; we act according to the odds of a successful outcome. But predicting probability depends on the information we have. In March this year, scientists appointed by the Japanese government warned of a massive earthquake in the Nankai Trough (“nankai mo”), and Kyoto University Professor Haruo Hayashi claimed there is a 60-70% probability of a magnitude 8-9 earthquake hitting the Nankai Trough within the next three decades. Magnitude 9 is huge, so since I have a house in the area, the prediction is worrisome.

However, Robert Geller, professor of geophysics at the University of Tokyo, finds the basis for the prediction faulty. The data, he notes, that the researchers base their predictions on focus on only the past few centuries — much too short a time span since the Earth is around 4.6 billion years old. In other words, making predictions based on such limited information is impossible. And expensive, since earthquake insurance premiums will go up, fueled by such official government claims.

Since I am on the subject of probability, Monty Hall, the legendary host of the game show Let’s Make a Deal passed away recently. Monty is probably best known for the probability problem that bears his name — the Monty Hall Problem. At the end of a show, the winners up to then would be given a chance for a really big prize, often a car. The contestant would be confronted with three doors. Behind two of them were goats, for example, and behind the third door was a brand-new luxury car. Needless to say, the contestant wanted the car. Of course the contestants could not see behind the doors but Monty could, so he had all the information. Monty would tell the contestant to pick a door. Suppose the contestant picked Door A. Monty, knowing behind which doors the goats and car were, would open Door B, behind which would be a goat. So we are only certain a goat is behind Door B. Monty would then ask the contestant the final question: Do you want to switch your answer to Door C or keep Door A? According to the probabilities involved, what should she do, stay with Door A or pick Door C?

Columnist Marilyn vos Santos, who reportedly had an IQ of 228, the highest ever recorded, wrote in her Parade Magazine column that the contestant should switch doors. She was immediately greeted by scorn and criticism from numerous mathematicians and statisticians for giving the wrong answer. Was she wrong? Try to figure out the answer and check this site for a good answer. https://gizmodo.com/heres-the-best-explanation-of-the-monty-hall-yet-1580031464

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