Life is full of random events!

Tossing a coin, throwing dice, and drawing numbers for a lottery are all examples of random events.

In this lesson, you will learn about dependent and independent events.

Courtesy of Pixabay

Sometimes an event can affect the next event.

For example, taking coloured marbles from a bag: as you take each marble, there are fewer marbles left in the bag, so the probabilities change.

We call this type of event a dependent event, because what happens depends on what happened before.

The other type of event is an independent event. Independent events are not affected by previous events.

This is an important idea! A coin does not "know" it came up heads before, so each toss of a coin is a perfectly isolated thing.

For example, you toss a coin and it comes up heads three times. What is the chance that the next toss will also be heads?

The chance is simply ½ (or 0.5) just like ANY toss of the coin. What it did in the past will not affect the current toss!

Some people think it is overdue to come up tails, but really the next toss of the coin is totally independent of any previous toss.

Let's look at a couple more examples.

If you tossed a coin and one six-sided die up in the air, the chance of getting heads on the coin and rolling a two on the die are independent of one another. What comes up on the coin has nothing to do with what comes up on the die.

Courtesy of Pixabay

Courtesy of Pixabay

Another example would be if you randomly chose a card from a deck, looked at it, put it back, and then chose another card out of the deck. Let's say you pulled the king of hearts out of the deck first and put it back. Because it is now in the deck and could possibly be picked again, the second card you pull is an independent event.

Independent events literally mean that whatever you do first has no affect on what you do second.

An everyday example of independent events would be if you had math homework and social homework each night and always finish both. You can either choose to do the math homework first or the social homework first. Doing one before the other makes no difference on the final outcome, because everything will be done.

Dependent Events

Dependent events, on the other hand, mean just the opposite. Two events are dependent if the outcome of the first affects the outcome of the second so that the probability is changed.

Let's go back to our card example. Let's say that on the first pick, I pulled the king of hearts again but this time did not put it back into the deck before I chose a second card. When I pulled out the first card, I had 52 choices. Because I did not return the card to the deck before I pulled the second card, I only had 51 choices for the second card. I have changed the chance of the second outcome. To put it simply, by doing one thing, I have had an effect on the other.

Courtesy of Pixabay

An everyday example of a dependent event is how much you earn working. The amount you earn depends on how many hours you work.

Let's try some examples to see if you can tell if they are dependent or independent events.

Look at the events below. Read through them first to decide if they are dependent or independent. Then, check your answers on the right!

A number cube is rolled twice.

It is raining outside, and the parade is cancelled.

The first roll of a number cube is 4, and the sum of the first two rolls is 5.

Joey got an A on his math test, so he will get an A on his science test.

  Self-check!