[This is a back-issue of one of this site’s newsletters]
Remember Linda?
Last week, I wrote:
Consider Linda (not her real name, since she’s not a real person). Linda is 30 years old, and completed aa liberal arts major at a well-known college, with high honours. While there, she was active in student politics, almost capturing the role of Student Guild President during her senior year. She also spent two years as secretary of the debating club. He best subjects were psychology, sociology and history.
Then I asked you to guess the probability that:
1) Linda works as a bank teller.
Go on, guess, write the probability down, then cover your guess.
Before I ask the next question, here’s a few articles I’ve posted online in the past week:
- My review of what is possibly the best times table tool I’ve ever seen.
- A simple word puzzle, based on tic-tac-toe.
- My article on how to draw an irregular tesselation got 14000 facebook likes. Check it out and tell me what I did right (or, share it on facebook and give it a few more!)
Go on, enjoy reading those articles! Linda will still be in your Inbox when you come back…
When you’ve finished reading, guess the probability that:
2) Linda is a bank teller who is active in the feminist movement.
Done that? Now: compare your two guesses.
Did you give 2 a higher probability than 1? People often do. My son said 50% for 1 and 85% for 2. But hang on, if Linda is a bank teller who is active in the feminist movement, then she’s certainly a bank teller. So 1 is true every time 2 is, and 2 is only true sometimes when 1 is.
Imagine you get a big blank dartboard. Or, draw this dartboard on a piece of paper. Draw a circle on the dartboard, and label it “bank tellers”. Then, draw a second circle, calling it “bank tellers who are active in the feminist movement”. This second circle should be a smaller circle, completely inside the first one – because, remember, every bank teller who is active in the feminist movement is also a bank teller.
Now, get a dart, write “Linda” on it, and throw it.
Can you see that the chance of hitting the small circle must be smaller than the probability of hitting the large circle? Even though our intuition says differently? You can’t hit the small circle without hitting the big one.
People are lousy at guessing probabilities. The more specific something is, the higher we intuit its chances to be, even though the chances actually get smaller. This sometimes leads us into erious trouble, taking on risks that are very unreasonable.
I wonder what life would be like, if people started adjusting their intuition with a little bit of hard probability logic? Or if that were impossible, if everyone at least became aware that most of their probability guesses are wrong?
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