Do you take into account probability when making decisions? Why do we make decisions that contradict probabilistic logic?

Understanding probability can be especially relevant to our daily lives because we make decisions based on our perception of probability all the time. However, our perception of likely outcomes is often mathematically irrational. This is because thinking in probabilities isn’t intuitive: Most people think in terms of binary categories of “yes,” “no,” and “maybe.”

Here’s why we make decisions that contradict probabilistic logic.

Understanding Probabilities

Probability allows us to manage uncertainty by measuring risks and putting possible outcomes in perspective. However, few people take into account probability when making decisions in real life. For example, the probability of getting in a car accident while driving to a beach is far higher than the probability of being attacked by a shark there, but we often—irrationally—fear the shark risk more.

Basic Probability

We can determine how mathematically likely an outcome is by setting up a fraction with the outcome we’re interested in on top and all possible outcomes on the bottom. For example, in a bag of 32 chess pieces, 16 will be pawns. The probability of pulling a pawn out of the bag will be 16/32, which reduces to 1/2, or 50%.

The probability of multiple independent events happening is the product of their probabilities. For example, in a bag of 32 chess pieces, the probability of picking a pawn out of the bag twice in a row (provided you put the first pawn back in the bag) is 16/32 x 16/32. When reduced to 1/2 x 1/2, the product is 1/4, or 25%. The probability of this happening three times in a row is 1/2  x 1/2  x 1/2, which equals 1/8 or 12.5%, and so on.

Sometimes, we’re interested in the likelihood of one of two mutually exclusive outcomes. In that case, option A or option B’s likelihood is the sum of their probabilities. For example, the likelihood of picking a pawn or a bishop out of the bag of chess pieces is 16/32 (probability of a pawn) + 4/32 (probability of a bishop). We can reduce this to 4/8 + 1/8, which is 5/8 or 62.5%.

Other times, we’re interested in the likelihood of one of two non-mutually exclusive outcomes. In that case, the probability of A or B happening is the sum of their individual probabilities minus the probability of both events happening. For example, the probability of picking a pawn or a piece (any piece) from the white set of chess pieces is 16/32 (chance of a pawn) + 16/32 (chance of a white piece) – 8/32 (the number of white pawns, which are already included in the calculation through the first fraction). When we reduce this to 2/4 + 2/4 – 1/4 it equals 3/4 or 75%.

Why Thinking in Probabilities Is Not Intuitive

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Darya Sinusoid

Darya’s love for reading started with fantasy novels (The LOTR trilogy is still her all-time-favorite). Growing up, however, she found herself transitioning to non-fiction, psychological, and self-help books. She has a degree in Psychology and a deep passion for the subject. She likes reading research-informed books that distill the workings of the human brain/mind/consciousness and thinking of ways to apply the insights to her own life. Some of her favorites include Thinking, Fast and Slow, How We Decide, and The Wisdom of the Enneagram.