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Meet Lucy.

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She was a math major in college,

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and aced all her courses in probability 
and statistics.

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Which do you think is more likely: that 
Lucy is a portrait artist,

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or that Lucy is a portrait artist 
who also plays poker?

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In studies of similar questions, up to 80 
percent of participants

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chose the equivalent 
of the second statement:

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that Lucy is a portrait artist 
who also plays poker.

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After all, nothing we know about Lucy 
suggests an affinity for art,

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but statistics and probability 
are useful in poker.

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And yet, this is the wrong answer.

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Look at the options again.

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How do we know the first statement 
is more likely to be true?

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Because it’s a less specific version 
of the second statement.

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Saying that Lucy is a portrait artist 
doesn’t make any claims

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about what else she might or might not do.

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But even though it’s far easier to imagine
her playing poker than making art

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based on the background information,

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the second statement is only true if she 
does both of these things.

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However counterintuitive it seems 
to imagine Lucy as an artist,

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the second scenario adds another condition
on top of that, making it less likely.

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For any possible set of events, the 
likelihood of A occurring

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will always be greater than the likelihood
of A and B both occurring.

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If we took a random sample of a million 
people who majored in math,

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the subset who are portrait artists might 
be relatively small.

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But it will necessarily be bigger

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than the subset who are portrait artists 
and play poker.

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Anyone who belongs to the second group 
will also belong to the first–

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but not vice versa.

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The more conditions there are, 
the less likely an event becomes.

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So why do statements with more conditions
sometimes seem more believable?

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This is a phenomenon known as 
the conjunction fallacy.

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When we’re asked to make quick decisions, 
we tend to look for shortcuts.

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In this case, we look for what seems 
plausible

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rather than what is statistically 
most probable.

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On its own, Lucy being an artist doesn’t 
match the expectations

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formed by the preceding information.

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The additional detail about 
her playing poker

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gives us a narrative that resonates 
with our intuitions—

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it makes it seem more plausible.

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And we choose the option that seems more
representative of the overall picture,

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regardless of its actual probability.

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This effect has been observed 
across multiple studies,

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including ones with participants 
who understood statistics well–

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from students betting on 
sequences of dice rolls,

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to foreign policy experts predicting 
the likelihood of a diplomatic crisis.

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The conjunction fallacy isn’t just a 
problem in hypothetical situations.

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Conspiracy theories and false news stories

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often rely on a version of the conjunction
fallacy to seem credible–

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the more resonant details are added 
to an outlandish story,

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the more plausible it begins to seem.

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But ultimately, the likelihood 
a story is true

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can never be greater than the probability 
that its least likely component is true.