Skip to main content
    Path to Science

    Thinking Dictionary

    Probabilistic reasoning

    What it is

    Probabilistic reasoning means asking "how likely?" instead of "yes or no?" You consider several possible explanations. You give each one a rough probability, meaning how likely it is, based on the evidence. Then you update those probabilities when new evidence comes in.

    Instead of "it's definitely X," you might think: "It's probably X, but it could be Y."

    Why it matters

    Life is full of uncertainty. Will the bus be on time? Is this symptom serious? Will the plan work? Treating these as simple yes-or-no questions can lead to bad decisions. Thinking in likelihoods helps you prepare for more than one outcome.

    Our gut feelings about likelihood go wrong in predictable ways. In a famous 1974 paper, the psychologists Amos Tversky and Daniel Kahneman described several mental shortcuts that lead to systematic errors.¹ For example:

    • Representativeness. We judge something likely if it looks like our picture of a typical case.
    • Availability. We judge something likely if examples come to mind easily.
    • Anchoring. We stay too close to a number we heard first, even an irrelevant one.

    The good news is that this skill can be learned. In a large forecasting tournament in the United States, people predicted world events. Three things made their forecasts better calibrated: a short training module on probability, working in teams, and tracking the best forecasters.² Being well calibrated means that your confidence matches reality. Of all the things you say are 70% likely, about 70% actually happen.

    Percentages vs "out of" numbers

    Research suggests that many people, experts included, find probabilities hard when they are given as percentages, and much easier as natural frequencies, which means counts of people, such as "8 out of 1,000."³˒⁴

    Here is an imaginary example to show why. Imagine a disease that 1 in 100 people have. A test for it catches 9 out of 10 people who have the disease. But it also wrongly flags about 1 in 10 people who don't have it. Your test comes back positive. How likely is it that you have the disease?

    Many people would say about 90%. Now think in counts. Picture 1,000 people:

    • About 10 have the disease. The test catches about 9 of them.
    • About 990 don't have the disease. The test wrongly flags about 99 of them.
    • So about 108 people test positive, and only 9 of them actually have the disease.

    That is fewer than 1 in 10. The counts make it clear. How common a condition is in the first place, called the base rate, matters a great deal. Studies suggest that giving information as counts, instead of percentages, makes this kind of reasoning much easier.³˒⁴

    In everyday life

    • Weighing explanations. Imagine you wake up with a headache. Most likely you're a bit dehydrated. Possibly you slept badly. Rarely, it could be something serious. Instead of picking one answer, give each a rough likelihood. Then watch for clues that shift the odds. Does a glass of water help? Did you sleep less than usual? Is it unlike any headache you've had before?
    • "Unlikely" things happen. A 1-in-10 chance sounds small. But if you face many 1-in-10 chances, some of them will come up. An unlikely event happening doesn't mean the estimate was wrong.
    • A positive test result. As the example above shows, what a positive test means depends on how common the condition is.

    The common trap

    The trap is thinking that "70% chance" is a hedge that can never be wrong. Probabilities can be checked, just not one at a time. You look at many predictions together. If only 4 in 10 of your "70%" predictions came true, you were overconfident.²

    Another trap is reading "unlikely" as "won't happen." Or reading "likely" as "certain."

    Some ways out:

    • Put a rough number on your beliefs, such as 50%, 70%, or 90%.
    • Turn percentages into counts: "out of 100 people like me, how many…?"
    • Ask how common something is in the first place before judging a single case.
    • Keep score of your predictions, and see how well you're calibrated.

    Try it

    For one week, before uncertain everyday events, write down a probability. Will the bus be on time? Will your team win? Will it rain tomorrow? Use only three levels: 50%, 70%, or 90%.

    At the end of the week, group your predictions by level. Did about 7 in 10 of your "70%" predictions come true? If all 10 did, you were underconfident. If only 4 did, you were overconfident. Keep going for a few weeks and see if you improve.

    Related concepts

    Confirmation bias · Placebo effect · Scientific models · Fermi estimation · Correlation vs causation · Scientific uncertainty · False positives and false negatives · Fast and slow thinking · Scenario planning · Cognitive shortcuts

    Sources

    1. Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 1124–1131. https://doi.org/10.1126/science.185.4157.1124

    2. Mellers, B., Ungar, L., Baron, J., Ramos, J., Gurcay, B., Fincher, K., Scott, S. E., Moore, D., et al. (2014). Psychological strategies for winning a geopolitical forecasting tournament. Psychological Science, 25(5), 1106–1115. https://doi.org/10.1177/0956797614524255

    3. Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: Frequency formats. Psychological Review, 102(4), 684–704. https://doi.org/10.1037/0033-295X.102.4.684

    4. Hoffrage, U., Lindsey, S., Hertwig, R., & Gigerenzer, G. (2000). Communicating statistical information. Science, 290(5500), 2261–2262. https://doi.org/10.1126/science.290.5500.2261