An athlete shoots 70%. If they shoot twice, what are the chances they make at least one? ðŸ¤”

Before answering, consider thinking. Daniel Kahneman has an entire book about Thinking, Fast and Slow. Fast thought is immediate. Slow is deliberate. Often â€˜thinking fastâ€™ about thinking fast and slow is that slow is better.

Thatâ€™s not the case. Lots of fast thought works well.

One problem with Kahnemanâ€™s book – which he admits, Kahneman is a scientist and when the evidence changes his understanding does too – is the social science replication crisis. Some studies donâ€™t repeat. Or repeat quirkily. For example: *Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.*

Which is more probable? (1) Linda is a bank teller. (2) Linda is a bank teller and is active in the feminist movement.

Thereâ€™s a lot in there. But our fast reaction goes something like: If this information is here it must be important. Answer number two. Thatâ€™s how we think.

But take the same *Linda is 31 years old…* prompt and ask this question: There are 100 persons who fit Linda’s description. How many of them are: (1) Bank tellers? __ of 100 (2) Bank tellers and active in the feminist movement? __ of 100.

Phrased that way the conjunction fallacy goes away.

**Thoughts are path dependent. Reframing changes the path. **

An athlete misses 30% of the time. If they shoot twice, what are the chances they miss both? ðŸ¤” Well they miss thirty percent of the time. To *miss both* it would be 30%*30%, which equals 9%.Â So to the original question, this athlete will make at least one more than ninety percent of the time.

If riddles are a good proxy, there are two tools: intuition and presentation. Intuition is internal. How many mental models do we have? How numerate are we? Whatâ€™s our (ongoing) education? Presentation is external. What are the norms? Whatâ€™s the phrasing? All framing is relative so what is this *relative to?*

Letâ€™s leave with one more. Historically category five hurricanes hit Beach City once every hundred years. What chance is there for a storm of that level in the next thirty years?

*Other examples for our intuition: **Birthday Bet**, Simpsonâ€™s Paradox. *

Also, this thinking and these riddles are courtesy of Michael Steiner’s podcast appearances. Sign up for Listen Notes and search him out. I enjoy [The Pathless Path](https://lnns.co/lGC0UYZr47A) & The Derivative.