Independence (statistics) facts for kids

Probability theory is a part of mathematics that helps us understand events that happen by chance. It looks at how likely something is to occur. When we talk about several events happening, we often assume that one event happening doesn't change the chances of another event happening.

For example, if you flip a coin, getting "heads" on the first flip doesn't change the chance of getting "heads" on the second flip. Each flip is a separate event.

What Are Independent Events?

Two events are called independent if the chance of one event happening stays the same, no matter if the other event has happened or not. Think of it like this: they don't affect each other at all.

How Do We Know if Events Are Independent?

We can tell if two events are independent if the chance of both of them happening together is equal to the chance of the first event happening, multiplied by the chance of the second event happening.

For instance, if you roll a dice and flip a coin:

• The chance of rolling a 6 on the dice is 1/6.
• The chance of flipping heads on the coin is 1/2.
• The chance of both rolling a 6 AND flipping heads is (1/6) * (1/2) = 1/12.

Since you can multiply their individual chances to get the chance of both happening, these two events are independent.

A Simple Definition

A famous mathematician named Abraham de Moivre once said: "Two events are independent, when they have no connection one with the other, and that the happening of one neither forwards nor obstructs the happening of the other." This means they don't help or hurt each other's chances of happening.

Examples of Independent Events

Coin Flips

Flipping a coin multiple times is a great example. Each flip is independent of the others. Getting heads on your first flip doesn't make it more or less likely to get heads on your next flip. The coin doesn't "remember" what happened before.

Rolling Dice

If you roll two dice, the number you get on the first die doesn't change the number you get on the second die. They are independent events.

Drawing Cards (with replacement)

Imagine you draw a card from a deck, note what it is, and then put it back into the deck before drawing again. Each draw is an independent event because you're always starting with a full, shuffled deck.

Related Ideas

• Conditional probability: This is about how the chance of an event changes if another event has already happened. It's the opposite of independent events.