8.05 Dependent and independent events
Events that happen at the same time
When we think of things happening, we know some things can't happen at the same time. You can't be sleeping at the same time as you are awake. If you are standing up, you are not sitting down.
Then there are things that may happen at the same time. You might be standing up, or you might be eating. It's also possible that you are standing up and eating.
In our first video, we will look at events where there can only be two possibilities.
Sometimes, such as when you throw a die, you have more things that could happen. A die has 6 sides. If we only have one die, then we can only roll a 1, 2, 3, 4, 5 or 6. We can't roll a 12, as we only have one die.
A deck of cards has 52 cards. Within a deck of cards, there are different colors, numbers and patterns. This means there are many possibilities of things that could happen. In the second video, we look at having different options, to see what is possible.
Examples
Example 1
Is it possible for the following two events to happen at the same time?
It is a Friday.
It is raining.
Example 2
A dog is randomly selected from the group of dogs shown.
Which two outcomes could happen at the same time?
When we think of the possibility of events we can consider if they can happen at the same time or not.
Independent and dependent events
An independent event means that the chances of that event happening are not changed by what happened before. For example, when we flip a coin, there is always a \dfrac{1}{2} chance that it will land on heads. It doesn't matter whether you tossed a head or tail before.
To see how this works, let's work through an example where you have four different colored lunchboxes and look at the chance of a particular color being chosen each day.
A dependent event means that the chance of that event changes depending on what happened before. For example, let's say you have an electronic claw machine game full of all different prizes. If you pull a toy car out, could someone else choose that same prize?
Let's look at your lunchbox colors again and see how the chance of picking a particular color changes when you don't bring them home at the end of the day.
Examples
Example 3
A teacher has a "prize bag" filled with different prizes. The students form a line to draw a prize from the bag at random. Once a student has drawn a prize, they take it back to their desk.
Are their selections independent or dependent?
Example 4
A card is randomly selected from a normal deck of cards, and then returned to the deck. The deck is shuffled and another card is selected.
Are the events of each selection independent or dependent?
To determine whether an event is an independent or dependent event:
- If the events are affected by what has already happened, they are dependent upon each other.
- If a previous event makes no difference to what can happen in the future, they are independent of each other.