Up to a certain point, humans have an intuitive understanding of basic probability. Toddlers can observe probabilistic patterns and grasp their meaning without any formal instruction, and we naturally use an internal process that approximates Bayesian inference to estimate physical states by combining previous knowledge with new sensory information.

Monty Hall Problem

In other situations, our intuition often leads us to the wrong conclusion. A classic example is the Monty Hall problem, in which the participant is presented with two options that intuitively seem equal, but in fact one of the choices is significantly more likely than the other to reveal the prize.

Compound Probabilities

But what about when we start looking at more complex problems?

At a certain point, even people who are familiar with statistics lose their intuitive understanding of the likelihood of a given event.

Try this riddle:

Imagine there are two boxes in front of you, both full of red and blue balls. You know that one of them has ⅔ red balls, and the other ⅔ blue balls—but you don’t know which is which.

You choose one of the boxes and start pulling out balls one at a time.

Each time you pull out a ball, you write down its color and return it to the box. After the 50th time, you count that 30 of the balls were red, and 20 were blue.

It’s easy to see that this box (Box A) is more likely than the other box (Box B) to be the one with ⅔ red balls—but by how much?

What’s the likelihood that the box you chose was the one with ⅔ red balls?

Before reading the answer, take a minute to think about it. What does your intuition tell you?

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Answer:

Most people intuitively think it’s around 60% to 80% likely.

But it turns out that it’s 99.9% likely that Box A is the one with ⅔ red balls.

Why do people tend to underestimate the answer? 

Because it’s hard for humans to intuitively understand the weight of accumulated evidence. Think of each time a ball is drawn as one snowflake: individually not very conclusive, but when enough of them accumulate they together have a much more substantial weight.

What Does This Teach Us?

By nature, human intuition has trouble accounting for the effect of many independent events occurring together. That’s why mathematicians have developed objective probabilistic methods to calculate the combined effect of multiple pieces of evidence.

When we become aware of our natural human biases, we can build a better system to overcome our inherent limitations.

Rootclaim uses proven probabilistic methods to calculate the combined effect of all the evidence, without relying on flawed human intuition.