When something extraordinary occurs, you might be tempted to say, just like me, that it must have “happened for a reason.” As in, it feels like there’s some magical force or hidden cause behind it—a series of coincidences that align in ways that seem too perfect to be random.

For instance, have you ever guessed the next song on your shuffled playlist? Or thought about someone just before they called you, making you wonder if there was some kind of telepathic connection between the two of you?

As surprising as these moments are, they’re not supernatural. They can actually be explained by what’s called the ‘Improbability Principle,’ introduced by British statistician David J. Hand. In simple terms, it means that highly unlikely events are pretty common.

To dig deeper into these unusual occurrences, Bored Panda got in touch with Márton Balázs, Professor of Probability at the University of Bristol.

“Coincidences are overwhelmingly random,” Balázs told us. But just because they’re random doesn’t mean they’re rare. “As also explained in the Improbability Principle, I believe that remarkable events occur for natural reasons far more often than due to some background common cause that we are unaware of.”

“Once we understand how enough number of trials will eventually bring up even the most unlikely events, we can find calm and reassurance in this knowledge. Which is far better than reaching out to unknown and mystic reasons, isn’t it?”

“Add to this human psychology,” says Balázs. “Unexpected coincidences are remembered long while everyday’s typical non-coincidences are not even recorded by the brain. Who cares about the thousands and thousands of telephone numbers I saw that don’t have my birthday in it? I will only notice the one that does.”

It’s worth noting that the Improbability Principle isn’t just a single rule. As David J. Hand explains, it’s actually a set of laws—kind of like Newton’s laws of motion or the laws of thermodynamics. But in this case, there are five.

The first is the Law of Inevitability, which says that one of the set of all possible outcomes has to happen. For instance, if you roll a die, it’s inevitable that it will land on one of the numbers between one and six.

The Law of Inevitability can pop up in other surprising ways too. Take the famous “birthday problem.”

How many people do you think need to be in a room before it’s more likely than not that two of them were born on the same day?

The answer is surprisingly low—just 23 people. With a group of 30, the odds increase to around 70%. And in a large gathering, like a conference with 1,000 attendees, it’s certain that at least two people will have the same birthday.

There are plenty of other things we assume are rare, yet happen far more often than we realize. It would be hard to list them all, but one of Márton Balázs’s favorite examples involves something as simple as flipping a coin.

Hungarian mathematician Pál Révész once asked students to either record the outcome of 200 coin tosses or, without flipping, to write down a sequence of Heads and Tails they thought would look realistic.

Not knowing which way each student went, Révész could tell who had “faked” their results. Why? Nearly everyone who made up the sequence on their own avoided including five or more consecutive Heads.

“It just feels so unlikely, totally unreal,” says Balázs. “But this is actually quite common with 200 coinflips; even runs of length eight or more occur at least once with a reasonable chance.”

Another of the Improbability Principle’s five laws is the Law of Truly Large Numbers, which states that even the tiniest chance of something happening becomes almost certain if you give it enough opportunities.

For instance, if you randomly generate a string of eight digits, you’d be shocked if it matched your birth date.

“But if you look through the infinite number of seemingly random digits in the decimal expansion of the mathematical constant pi, you will find your birth date eventually,” says Hand. “For example, my birth date, 30 June 1950—30061950—starts at digit 190,652.”

The third law, the Law of Selection, says that we can make events as likely as we want by choosing after the fact. For example, you can guarantee that the next roll of a die will be no higher than the last if you only consider rolls that show a six.

The next law, the Law of the Probability Lever, shows that small changes in circumstances can drastically alter the odds. A well-known case of this is the “black swan” phenomenon in the financial world, where extreme events like market crashes are difficult to predict due to their unexpected nature.

The final law, the Law of Near Enough, says that if you broaden your definition of what counts as a coincidence, you can make it as likely as you want. “There’s a one in 365 chance that my birthday is on the same date as that of a randomly chosen reader,” says Hand. “But a one in 52 chance that it’s in the same week. And a one in 12 chance that it’s in the same month.”

Probability is a fun area of mathematics, but it’s not always easy to grasp, which is why it often leaves people puzzled. For instance, many confuse probability with possibility.

Some might say there’s a 50/50 chance of waking up to $30 million on your bed, but that’s not accurate. Possibility means something can happen, but doesn’t predict if it will. So, while it’s possible to wake up a millionaire, it’s not probable. Probability means something is both possible and likely to happen.

“If the above wouldn’t be enough, humans are also rather bad with independence,” says Balázs. “A friend once told me when cycling, ‘This month I already had two nails in my tyre. I’m sure this will stop now, I've had enough bad luck.’”

“Well, for such a scenario we have this highly accurate and beautiful model called the Poisson process, and it tells us that past nails bear no information whatsoever for future punctures.”

“The chance my friend will have another one in his tyre tomorrow is the same whether he already had 0, 1, 2, or any number of nails this month. I find this yet another fascinating fact of the world around us, and only wish more people would think the same!”

Say what you will about math—it might be tricky, but it sure knows how to blow your mind in the coolest ways.