Random Numbers Explained: Fair Picks, Dice and Lotteries

A random number is one that cannot be predicted, where every allowed value has the same chance of coming up. If you pick a whole number from 1 to $n$ fairly, each one has probability $\frac{1}{n}$. Random numbers are used for games, raffles, lotteries, experiments and fair sampling.

Fair means equally likely

Rolling a fair six-sided die gives each face a probability of

A random number generator should behave the same way: choosing from 1 to 100 gives each number a $\frac{1}{100}$ chance.

With or without repeats

• With repeats (like rolling a die again and again): every draw is independent, so the same number can appear twice.
• Without repeats (like lottery balls or picking raffle winners): once a number is drawn it is removed.

How likely is a lottery win?

Choosing 6 numbers from 49 without repeats, where order does not matter, gives

possible tickets, so one ticket has about a 1 in 14 million chance.

Streaks happen

In 10 coin flips, a run of four heads in a row is common. Real randomness produces clusters, and people often mistake these for patterns. Past results do not change the next one; that mistake is called the gambler's fallacy.

Pseudo-random vs secure random

Computers use algorithms to make numbers that look random. Ordinary ones are fine for games; cryptographically secure generators, like the one in modern browsers, are designed so no one can predict the next value, which matters for fair draws.

Common mistakes

• Thinking a number is "due" because it has not come up for a while.
• Forgetting to remove numbers when picking without repeats.
• Using "pick a number" in your head: people are bad at being random and avoid round numbers.

Practice questions

1. What is the chance of picking 7 from the numbers 1 to 20?
2. Is rolling two sixes in a row less likely than rolling a 3 then a 5?
3. How many ways are there to choose 2 winners from 10 entries?

Answers: 1) $\frac{1}{20}$ 2) No, both are $\frac{1}{36}$ 3) 45

Draw fair numbers with the random number generator, work out dice odds with the dice probability calculator, and count lottery combinations with the permutation and combination calculator. See also probability basics.

Frequently asked questions

Open the calculator →