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A letter in the FT is still 'doing my head in'! Enjoy.
Sir, I think that most of your readers must have heard of the Monty Hall problem many times (“Stick-or-switch inspires an onion of a puzzle”, Tim Harford, October 7). Here is a somewhat subtler puzzle for them to ponder on Saturday morning.
You are presented with two envelopes and told that one contains twice the amount of money than the other one. You pick one. The host opens the other one and shows that it contains $12. You can now change your mind and go with the opened envelope and win guaranteed $12 or you can remain with your first choice. In the latter case, the unopened envelope contains either $6 or $24 dollars with equal probabilities, so the expectation value is $15, which is $3 more than the guaranteed $12. So, should you change your mind or not?
The failure of the majority of people in understanding the Monty Hall and related problems is often taken as an illustration about the poor intuition humans have about probability theory. But humans per se also have a very poor intuition about numbers and can count to about five without any formal education. But speak to any 14-year-old and they have a pretty good understanding of what a thousand is.
It is for purely historical reasons that probability, combinatorics and statistics are relegated to optional courses taught at the end of secondary education, while we teach quadratic equations and basic trigonometry as basic maths. Taking probability theory as a core maths topic could reduce the number of problem gamblers and reduce the societal impact of terrorist attacks, in addition to drawing more children to mathematics with its truly puzzling puzzles.
Anže Slosar
London SE13, UK