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

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

Thatâs not the case. Lots of fast thought works well.

One problem with Kahnemanâs 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 donât 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.

Thereâs a lot in there. But our fast reaction goes something like: If this information is here it must be important. Answer number two. Thatâs 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? đ¤ 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? Whatâs our (ongoing) education? Presentation is external. What are the norms? Whatâs the phrasing? All framing is relative so what is this *relative to?*

Letâs 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**, Simpsonâs 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.