Puzzle 4 – Reasoning with Probabilities
This is the most often-cited example of a fallacy in reasoning about probabilities originating with Amos Tversky and Daniel Kahneman called the conjunction fallacy.
In studies, 90% of people choose ‘Linda is a bank teller and is active in the feminist movement’ rather than ‘Linda is a bank teller’. But if you think about it more carefully it’s clear that the probability of two events occurring together (in “conjunction”) is always less than (or equal to) the probability of either one occurring alone.
For example, even choosing a very low probability of Linda being a bank teller, say Prob(Linda is a bank teller) = 0.05 and a high probability that she would be a feminist, say Prob(Linda is a feminist) = 0.95, then Prob(Linda is a bank teller and Linda is a feminist) = 0.05 × 0.95 or 0.0475, lower than Prob(Linda is a bank teller).
The other problem is the classic – and very difficult – Monty Hall Problem, explained here: