Why do we care about probabilities?

The useful aspect of our fundamental question
In what real world contexts is it both practical and useful to attempt to estimate numerical probabilities?
is naturally related to the question of why we care about probabilities. Obviously this is context-dependent, but can we give a general categorization of reasons?

Everyday uses

We have collected several types of data concerning where people think about chance in everyday life. But it is surprisingly hard to categorize the why's. Some of the search queries suggest a future decision: More frequent are queries that might be termed "casual curiosity": Most of the references to chance in tweets and blogs could be described as "commentary" on past or possible future events: These "commentary" or "casual curiosity" uses I will call narrative, and are a surprisingly common way we engage chance in everyday life. Incidently the type of situations that feature in the "what would you do in this situation" problems discussed in psychology (e.g. in Kahneman's Thinking, Fast and Slow) almost never appear when we search through individuals' unprompted mentions of chance or probability.


To many academics, the first reason that may come to mind is that we care about probabilities in the context of making a decision. Hearing "70% chance of rain" might prompt a decision to carry a raincoat or cancel a picnic. Almost any decision to do something involves a comparison between what is likely to happen if you do it, and what is likely to happen if you don't.

So it might be worthwhile to bring some "everyday decision theory" into a first course on Probability. In my Berkeley course I do a short theatrical piece: I open the annual letter sent to California homeowners reminding them that regular insurance does not cover earthquakes and inviting them to buy specific earthquake insurance, for about $1,800 in my case: I ask the class how should I decide whether to write the check or discard the letter?

Other topics within these pages are related to decision making, for instance

Probability in Science

The well known historical science-oriented insights involving probability -- Maxwell's statistical mechanics, Einstein's treatment of Brownian motion as arising from molecular bombardment, and population genetics refuting an objection to "evolution by natural selection" -- were definitely about understanding or explanation of some natural phenomenon. I distinguish this from the narrative use which just comments on some chance effect without seeking to explain further.

The "coincidences are more likely than you think" saying is another kind of explanation, saying explicitly that some things are "just chance".

Exploiting randomness

Chance usually refers to what is outside our control, but there are a few exploiting contexts where we deliberately introduce randomness. For instance: Queueing theory and various other parts of Operations Research deal with models of engineered systems subject to uncertainty. Even though here the randomness is outside our control, we can design a system to be optimal in some way based on a model of this randomness. We are exploiting the statistical regularity in the same way that we exploit knowledge of the laws of physics.

My categorization

The discussion above prompts me to suggest four overlapping reasons for caring about chance. The reader could look at our list of contexts where we perceive chance to judge how reasonable this categorization is. Of course many contexts involve several of these reasons, as illustrated next.

The risk industries

The insurance and finance industries are essentially about risk. From the customer's viewpoint there is a decision under uncertainty -- whether to invest in stocks or to buy life insurance depends on our assessment of likelihoods. From the industry's viewpoint there is a mixture of reasons; exploiting the fact that people seek to offload or take on risk, and understanding via historical data the likely payoffs.