The problem (set on 26 March 2010) was this:

*You choose eight different books randomly from a library shelf. If you turn to the same numbered page in each book (for example, page 5), how likely is it that on at least two of these pages the text will start with the same letter?*

For all the books to be different you need all these things to happen, so you multiply together the probabilities: 25/26 X 24/26 X 23/26 X 22/26 X 21/26 X 20/26 X 19/26, which equals approximately 0.3. So, the probability of them not being all different is 0.7.

Why is this so different from my experimental result? This is because of the assumption that all letters are equally likely. This is clearly not the case. In my trials I did not have any examples of the first letter being *x* or *z* (I didn’t use algebra books!). And certain letters, such as *t*, *a* and *s* turned up much more frequently than 1 in 26. This increases substantially the probability of letters being duplicated.

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