Probability Expression Miscommunication
Words such as 'likely' and 'slim chance' can mean different things to different readers. Jones reports interpretations ranging from 1% to 85% across different expressions. Clarify the intended probability and its basis; his preference is to use numbers during analysis and avoid unsupported precision in reports.
THE IDEA
EXERCISE 31 Safecracker I
A fabulous diamond is kept in a safe behind five doors, each secured by a combination lock. You are a thief seeking to steal the diamond. All five doors have exactly the same kind of lock made by the same company but with different combinations. In your career as a thief, you have encountered this lock ten times. Only once—the last of those ten times—have you failed to open the lock. Disregarding all factors except the combination lock, what is the probability, expressed as a percentage (20%, 50%, 80%, etc.), that you will get through all five doors and steal the diamond? Write your percentage on a sheet of paper.
BEFORE CONTINUING, WRITE DOWN A PERCENTAGE THAT REPRESENTS THE PROBABILITY YOU WILL STEAL THE DIAMOND.
Next to your percentage, write an adjective or adverb-adjective that you think best characterizes the percentage, such as unlikely, possible, very likely, almost certain.
BEFORE CONTINUING, WRITE NEXT TO THE PERCENTAGE AN ADJECTIVE OR ADVERB-ADJECTIVE THAT CHARACTERIZES THE PERCENTAGE. (KEEP THE SHEET OF PAPER. WE’LL REFER TO IT LATER.)
People commonly make inordinately casual use of probability expressions, such as most likely, in all likelihood, may, slim chance, and certainly, under the mistaken assumption that these expressions mean the same thing to everyone.
“What are our chances of being on time for our appointment if we stop for dinner?” asks a wife of her husband.
“Fair,” he replies.
“Okay,” she says, “then let’s stop here.”
After dining, they arrive at their appointment a half hour late. She’s upset and complains to her husband, “I thought you said we’d be on time!”
He’s shocked. “I never said anything of the kind.”
“You said our chances were ‘fair.’ “
“Yeah, like we wouldn’t be on time!”
People can interpret the same probability word differently. Jones gives a range of 55 to 85 percent for likely, and 1 to 15 percent for a slight chance of rain. If you’re skeptical of these ranges, do your own survey. Ask your family or friends what various adjectival probability terms mean to them. You’ll find their responses enlightening and entertaining.
Whether we are analyzing a problem alone or collaborating with others, we should make it a rule to highlight all probability expressions and translate them into percentages. I’ve italicized certain words in the following excerpt of an article in Firehouse magazine to show you what I mean:
The U.S. Fire Administration’s Juvenile Firesetter Programs show that the greater percentage of fires are set by young children in the five to nine age group. In addition, these programs indicate that five- and six-year-olds may not be capable of understanding the concept that a single match can destroy a house. Therefore, not only do young children represent the highest risk group with respect to their involvement in firestarting, but they are also the most likely victims of fire injury and death…. Unlike elementary school children, who may be involved in only one or two unsupervised firestarts, psychiatric patients are more likely to be involved in several incidents of firesetting behavior. In addition, the fires set by children with psychiatric diagnoses are more likely to cause serious damage requiring firefighter suppression.
This is a typical example of casual use of probability expressions. If they weren’t highlighted, they would hardly be noticed. Yet because they have significant impact on the meaning of the text, it is fair to question what precise probability the authors meant to convey in each case.
[S]ix-year-olds may not [understand] that a single match can destroy a house.
What does “may” mean here? Is the claim about some children’s ability, the proportion of children who lack that ability, or uncertainty in the evidence? Those are different questions. If the intended comparison is a 50 percent share versus a 1 percent share of children, the prevalence differs greatly. The wording alone does not supply either estimate.
[Y]oung children … are the most likely victims of fire.
Does “most likely” specify a probability, or only rank this group’s risk above that of other groups? The highest risk among several groups need not exceed half.
I repeat my advice. When we are analyzing a problem or drafting a report, we should convert all probability expressions into percentages… but only in the analytic phase. My recommendation is to avoid percentages in final written products unless—and such instances are extremely rare—the numbers are based on definitive evidence and precise calculations. The biggest challenge in dealing with probability is conveying through language what a probability represents without using a percentage. But that’s a subject for a book on writing, not a book on structuring analysis. (One solution, favored by some writers and strongly opposed by some others, is to identify up front for the reader what the various probability expressions used in a written product represent in percentages, e.g., “probable” = 85%, “unlikely” = 20%, etc.)
When to use it
In a business meeting, explain both the estimate and its basis—for example, a 70% chance of meeting a deadline—when that level of precision is justified.
When reading reports, highlight all probability expressions and assess their numerical meaning to evaluate the strength of conclusions.
When a forecast supports it, pair a phrase such as 'slight chance' with the numerical estimate, such as a 10% chance of rain.
When collaborating on a decision, ask team members to translate their probability expressions into percentages to align understanding.
FROM THEORY TO EVERYDAY LIFE
In practice
The Dinner Appointment Misunderstanding
In the dinner dialogue, the husband and wife attach different meanings to 'fair'. One might imagine a 20% chance of arriving on time versus a 70% chance. Those figures illustrate the possible gap; the dialogue does not give either person’s numerical estimate.
Firehouse Magazine Excerpt on Juvenile Firesetters
The excerpt uses 'may', 'most likely' and 'more likely' without explaining their intended meaning. A reader might imagine 1% or 50%, but the wording alone establishes neither. Clarifying whether a claim concerns prevalence, a comparison between groups or uncertainty in the evidence comes before assigning a number.
A MOMENT TO REFLECT
Put it to work.
Think of a recent conversation where someone used a probability expression like 'likely' or 'unlikely'. What percentage would you assign to that expression, and would others agree?
When planning a project, which probability words do people use? Could you agree on their meanings using percentages, ranges or clearly defined terms?
In the safecracker exercise, what did you assume about the chance of opening each lock and the relationship between attempts? How did you choose a word for your estimate?
CONTINUE THE CONVERSATION
Source texts
- The Thinkers Toolkit by Morgan D Jones