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A likely trade-off
Probabilities are hard to understand, but some mistakes may not be what they seem
Chance is a bit of a slippery concept for many of us. We can grasp that, if we toss a fair coin, the likelihood of heads (or tails) as a result is about 50%. If we roll a die, we also understand that each number between 1 and 6 is equally likely to turn up. We may even be able to work out that, when a colleague informs us that her new neighbours have three children, the chance that these all have the same gender is 1 in 4.
Yet even only slightly more complicated questions tend to faze us. If there are three of you in a room, the chance that at least two people have the same birthday is quite small — we get that intuitively. (It is in fact less than 1%.) But how many people would there need to be in a room for it to be almost certain that at least two of them share a birthday — say more than 99%? Our intuition might suggest something like 99% of 365. That feels nicely symmetrical: with three it’s less than 1%, so with about 365–3 it should be more than 99%. But unless you know the answer or are a probability calculus wizard, you might be surprised to learn that the correct answer is 57. (See the Wikipedia entry on the Birthday Problem to find out more.)
