What's the chance that a random woman you meet on the street is exactly 170cm tall? The question seems impossible to answer, but luckily maths can help. It tells us that the heights of people follow a probability distribution known as the normal distribution (also sometimes called a Gaussian...

Probability distributions turn up in all areas of science (and in many Plus articles) so we've decided to have a closer look at them. The short explainers below explore what a probability distribution actually is, visit some of the most commonly used distributions, and a few important concepts in...

Suppose that during a given time period an event happens on average times. For example, you might know that on average you'll see three new posts on your social media feed per minute. This doesn't mean that the event will occur at regular intervals: seeing three posts a minute on average doesn't...

Probability distributions describe processes that can have more than one outcome which you can't be sure about in advance. An example is rolling a die. There are six possible outcomes, namely the numbers 1 up to 6. As long as the die is fair, these are all equally likely to happen — you're just as...

Suppose that during a given time period an event happens on average times. For example, you might know that on average you'll see three new posts on your social media feed per minute. This doesn't mean that the event will occur at regular intervals: seeing three posts a minute on average doesn't...

Suppose that during a given time period an event happens on average times. For example, you might know that on average you'll see three new posts on your social media feed per minute. This doesn't mean that the event will occur exactly times during every such time period: sometimes you might see...

In our brief introduction to probability distributions we talked about rolling dice, so let's stick with that example. Imagine I roll a die three times and each time you try and guess what the outcome will be. What's the probability of you guessing exactly k rolls right, where k is 0, 1, 2 or 3? ...

It's Christmas eve! On this very special day we thought we'd explore a very special theorem. Its initial proof, first announced in 1981, ran to over 10,000 pages, spread across 500 or so journal articles, by over 100 different authors from around the world, was without precedent. It must be counted...

Group theory is essentially the study of symmetry. It underpins much of modern mathematics and is also hugely relevant to other areas — from physics to computer science. And although the field is over two hundred years old, it's still a vibrant and dynamic area in which exciting things are...

Cheryl PraegerIn Yesterday's door of the Plus advent calendar, we found out what a magician can do with a card shuffle. But what might a mathematician do when shuffling cards? To find out we asked Cheryl Praeger, from the University of Western Australia. It was Praeger who first intrigued us in...