Conjunction Fallacy

“A detailed story sounds persuasive. Can it be more likely than a broader version of that same story?”

01 / PLAINLY

What it means, plainly

Two things happening together cannot be more likely than either one alone, even when the combined story seems to fit better.

02 / CONTEXT

A little more

The probability of A and B occurring cannot exceed the probability of A alone. Yet a representative description can make the more specific combination feel more plausible.

03 / WHY IT MATTERS

Why it matters

Persuasive detail can make a narrow forecast look more likely than the broader category that necessarily contains it.

04 / EXAMPLE

A familiar example

“Works at a bank and is active in environmental causes” cannot be more common than “works at a bank,” because the first group sits inside the second.

05 / LIMIT

What it does not mean

It is not an error to say the combined story fits better; the mistake is turning that fit into a higher probability.

06 / NOTICE

Notice it in your day

Write one category, such as “student,” and another that adds a trait, such as “student and musician.” Draw which set must sit inside the other.

FINAL NOTE

The idea worth keeping

Draw the sets: if one option is contained within another, it cannot include more cases.

QUESTIONS / 02

Questions people still have

Why can the more detailed option sound better?

Its details may feel representative and form a coherent story even though they narrow the possible set.

Does a better fit mean a higher probability?

No. Fit describes resemblance or coherence; probability must also respect that the combined group sits inside the broader one.