COVID-19 and Probability

This was posted by a Facebook “friend” (who is among many on FB who seem to believe that figuratively hectoring like-minded friends on FB will instill caution among the incautious):

The point I want to make here isn’t about COVID-19, but about probability. It’s a point that I’ve made many times, but the image captures it perfectly. Here’s the point:

When an event has more than one possible outcome, a single trial cannot replicate the average outcome of a large number of trials (replications of the event).

It follows that the average outcome of a large number of trials — the probability of each possible outcome — cannot occur in a single trial.

It is therefore meaningless to ascribe a probability to any possible outcome of a single trial.

Suppose you’re offered a jelly bean from a bag of 100 jelly bean, and are told that two of the jelly beans contain a potentially fatal poison. Do you believe that you have only a 2-percent chance of being poisoned, and would you bet accordingly? Or do you believe, correctly, that you might choose a poisoned jelly bean, and that the “probability” of choosing a poisoned one is meaningless and irrelevant if you want to be certain of surviving the trial at hand (choosing a jelly bean or declining the offer). That is, would you bet (your life) against choosing a poisoned jelly bean?

I have argued (futilely) with several otherwise smart persons who would insist on the 2-percent interpretation. But I doubt (and hope) that any of them would bet accordingly and then choose a jelly bean from a bag of 100 that contains even a single poisoned one, let alone two. Talk is cheap; actions speak louder than words.

2 thoughts on “COVID-19 and Probability

  1. You’re right, of course, given that the outcomes are either death or you get to eat a jelly bean and survive. A more interesting case is to offer the eater $1 million if he eats a jelly bean and survives. I suspect a whole lot of people would choose to eat a jelly bean. It would be interesting to ask a large random sample of people what minimum amount of proffered money would be required to get them to eat a randomly selected jelly bean. I’d like to see a distribution of their answers.

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  2. I’d like to see that distribution, too. Though I would be skeptical of it. It would be biased downward; that is, in actual cases (rather than hypothetical ones), the price of eating a jelly bean would rise considerably for most respondents. Also, responses would be determined by (a) respondents’ preferences for living over dying and (b) their estimates of the net present value of the earnings that their families or loved ones would lose. The numbers would approximate NPV x 1 (the cost of dying), not NPV x “probability” of dying.

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