Following up on smijer's Let's Make A Deal post, I'll continue with a couple of oldies. These examples aren't really puzzles. Rather, they're questions that Amos Tversky and Daniel Kahneman posed to participants in experiments aimed at understanding how well people reason. Kahneman won the Nobel Prize in Economics for this body of work a few years ago.

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 of the following is more probable?

1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.

Most people say that the second description is more probable than the first.

Please rate the probability that the following event will occur next year...

1. A massive flood somewhere in North America next year, in which more than 1,000 people drown.

2. An earthquake in California sometime next year, causing a flood in which more than 1,000 people drown.
   

Most people say that the second event is more probable than the first.

Discussion below. . .

For those of you with logical minds and those of you who have guessed that there's some sort of trick involved, you've realized that the first statement in each case is more probable than the second (though it turns out that there's no trick). In mathematical terms, we can put things pretty concisely: P(A) <= P(A & B). For example, if we know that it's going to rain with some probability, then adding further conditions, such as that the grass will get wet, can't increase that probability, even if those other conditions inevitably hold, because the probability that it's going to rain already includes those extra other things.

Tversky and Kahneman were interested in biases in our reasoning. I wish I had the time and background to explain these biases, but I don't have a sufficiency of either; I think even without explanations it's interesting to know that, for some kinds of problems, we're not very good at coming up with the right answers.