Likely, unlikely, certain and impossible

Author: Stephanie Glen

I live in Jacksonville, Florida, where the odds of a hurricane on any given day are “improbable“. But does that mean I shouldn’t stock up on hurricane supplies and have an emergency preparedness plan? Far from it. Hurricane Irma blew through my city in 2017, causing around $85 million in damage and the worst flooding in the city’s 150 year history. 

The key here is the word “improbable.” In everyday use, if you tell someone the chances of rain are improbable today, they hear “it isn’t going to rain.” But if you tell a mathematician that same thing, they’ll carry an umbrella. Or possibly not, depending on what their definition of improbable is.

And therein lies the problem with terms in probability such as: likely, unlikely, certain, and impossible. Those loose definitions that mean something different not just from one layperson to the next, but from one mathematician to the next. As far as words like likely and unlikely, we can probably delete those from our probability vocabulary, because probability should never be defined in terms of being likely, or not (Deborah Mayo). 

So let’s take a look at improbable, certain and impossible a little more closely.


“You have to decide two things…what is your definition of likely or probable and conversely what is your definition of improbable? (UDEL)”

An “improbable” 28-second earthquake in L’Aquila, Italy killed 297 people in 2009 (and led to the conviction of seven scientists for manslaughter). Many people heard the word improbable and equated it to not likely. This is not surprising, because the general definition of the word, according to Google is “not likely to be true or happen.” However, in terms of probability, “improbable” usually means a fair chance of happening.

In David Hefland’s seminal book A Survival Guide to the Misinformation Age: Scientific Habits of Mind, he states that “Improbable things happen all the time and, Rare events are not necessarily rare at all” (p.144). But how exactly do we quantify an improbable event? That simple question is not easy to answer. Ask a statistician and you’ll get a response somewhere around a 20% chance; Depending on who you ask, that probability could be as high as 25.3% or as low as 10.6% (Hillson, 2005). Other words that have a fairly wide interval:

  • Highly probable: 64.2% to 78.3%
  • Probable: 47.5% to 66.7%
  • Highly unlikely: 9.8% to 23.3%

Oddly enough, “better than even” was defined in Hillson’s survey as a probability of anywhere between 47.1% and 65.6% (think about that for a second). 

Certain and Impossible

A strict definition for improbable is impossible to pin down, or is it? By “impossible” I mean “it’s not going to happen, Lad.” But am I correct to use that particular word? Unfortunately, I’m not. What I should say is “There is a 0% chance of pinning down a definition for improbable.” But is that even correct? 

Yesterday, when I checked my weather app, it said there was a 0% chance of rain. Which should mean impossible, yet I got drenched on a walk in the park with my dog. What I should have realized is that the definition of impossibility depends on what the app meant by 0%. Did it mean:

  • Mathematically, the probability is zero?
  • Mathematically, the probability is close to zero?
  • The event (rain) has never happened before under the expected weather conditions, so the probability is zero (but this is fluid and could change after the weatherman’s coffee break and another gander of the data).
  • No idea at all, let me put a placeholder there while we figure this front out.

Alas, if you were reading this blog post to pin down a definition for any of the loose terms in the title, I’m sorry to disappoint. Perhaps it’s because statisticians think in confidence intervals and margins of error that they are hesitant to formulate agreed-upon definitions for certain words. Although it’s likely (probable?) that mathematicians think in numbers and not words. Of that, I’m almost certain.

Describing probability: The limitations of natural language

Top stories of 2017: Irma’s rain, floodwaters damaged homes …

The Aftershocks

FRONTIERS OF SCIENCE: Scientific Habits of Minds


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