The other day, I went to Chadstone with the intention of buying a particular book. I believed that it would cost $19.95. Before I left the house I put the exact change in my pocket, because I like to be able to pay for the things that I intend to buy.

On the way to the bookstore i found $4 on the ground. There was no one else around, but there was a sign nearby saying that 'the Chadstone lost and found service was closed for the day, and that if you find small amounts of money abandoned on the ground you should just keep it'. That rather convenient sign allowed me to pocket the money without risk of damage to my morality.

I soon reached the large multi-level bookstore and located my intended purchase. But to my horror, the price tag read $23.95. Thankfully, it only took me 15 minutes to realise that despite the price increase I still had the exact change necessary for my purchase. Lucky I found $4.

By the way, the book was called "101 Amazing Things That Are Unlikely To Happen At Any Given Moment" written by Dr U.R. Fewlich

What are the chances? Surely, that is too amazing to have been a coincidence.

The probability of my amazing coincidence occurring to me that day is the probability of needing an extra $4 multiplied by the probability of finding $4 multiplied by the probability of seeing some rather unlikely 'finders keepers, losers weepers' signage. It would be fair to assume that the probability would be pretty damn small, so for the sake of argument let's say that the probability is 0.01%

That is pretty damn improbable. The problem is, that I only define the event as amazing after it has happened.

There are many more things that would count as amazing coincidences:

- Finding a free copy of that book, allowing me to spend my money on ice cream.

OR

- Everyone in a lecture at uni receiving a call on their mobile phone at the exact same time

OR

- Discovering that everyone in Wagga Wagga with the name Lorenzo just happens to have the same birthday, except for one guy who was swapped with a Lorenzo at birth. His real name was supposed to be Jim.

OR

- Finishing Super Mario Brothers at your first attempt while sitting in an Italian restaurant that just happens to be owned by a man who has a brother.

Let's assume that there is also a 0.01% chance of each of these events occurring. We now have five events, any of which occurring alone count as an 'amazing coincidence'. To find the probability of a logical disjunction we add together each of the individual probabilities:

0.01% +0.01%+0.01%+0.01%+0.01% = 0.05%

The chance of one of our five coincidences is still small, but not as small as the one very specific event that we were first concerned with.

Now, the number of events that will lead us to exclaim "how extraordinary!" is more than 5. It's more than 101. It's infinite!

So that means there is a 100% certainty that amazing coincidences will occur sooner or later.

If my clearly fictional book buying coincidence hadn't of happened, something else would have. But I don't spend time thinking about the amazing things that didn't happen. Nor do I spend time thinking about all the probable things that did happen.

So the lesson here is...umm...ergh...you can count anything you like as being amazing, but it's a good idea to take extra cash to the shops.