A distribution is the full picture of a random variable: every value it can take and how probable each one is. A handful of standard shapes describe a huge range of real situations, so learning them is like learning the common chords of chance.
The uniform distribution
The simplest shape is uniform, where every outcome is equally likely: a fair die, a fair spinner, a well-shuffled card. Nothing is favoured; the probability is spread evenly. It is the natural starting point and the picture of pure, unbiased randomness.
The binomial distribution
Count the successes in a fixed number of independent yes/no trials (heads in ten tosses, defective items in a batch) and you get the binomial distribution. It is peaked around the expected number of successes and tapers off to either side: ten fair tosses most often give four, five, or six heads, and only rarely zero or ten. It governs anything built from repeated all-or-nothing chances.
The normal distribution
The most important shape of all is the normal distribution, the famous symmetric bell curve. It clusters tightly around its mean and thins out into two tails, and it is fixed by just two numbers: the mean (where the peak sits) and the standard deviation (how wide the bell is).
For a normal distribution, about of the values fall within one standard deviation of the mean and about within two: a rule of thumb worth remembering.
Why the bell curve is everywhere
Heights, measurement errors, test scores, and countless other quantities follow a normal curve, and there is a deep reason. The central limit theorem says that when many small, independent effects add together, their sum tends toward a normal distribution: whatever the shapes of the pieces. Since so much in nature and society is a sum of many little influences, the bell curve emerges again and again. It is the reason the normal distribution sits at the centre of statistics, and a fitting place to end: from counting single outcomes, we have arrived at the shape that describes whole populations of chance.