Lesson video

Hi, my name is Mr Chan.

And in this lesson, we're going to learn how to draw a tree diagram for independent events.

Let's start with an example.

A bag contains four pink and three blue counters.

A counter is chosen at random and then replaced.

Then another counter is chosen at random.

Draw a probability tree diagram for the possible outcomes.

So here's a diagram to represent our bag of counters.

We've got four pink and three blue.

And we're going to pick out the counters twice.

So it does tell us the counter is chosen random and then replaced.

Then another counter is chosen at random.

So when we choose our counter first, we've got a probability of picking out a pink counter or a blue counter.

So that's the beginning of our tree diagram.

So we have in the bag four pink counters out of a total seven counters altogether.

So the probability of picking out a pink counter will be four out to seven, four sevenths.

Similarly, with our blue counters, we have three out of the possible total of seven.

So the probability of picking out a blue counter, we put on the tree diagram as three sevenths, and we label those probabilities on the branches of the tree diagram.

Now, our second picking out to the counter will involve either picking out a pink account or a blue counter again.

And we draw our branch from the pink counter for our second pick.

So if in the first pick we picked our pink counter, the important thing here is that with the pink counter has been replaced back into the bag.

So on our second pick, we are still going to have four out of seven pink counters and three out of seven blue counters.

So the probabilities will remain the same.

Similarly, if on our first pick, we picked out a blue counter.

It does tell us that the blue counter is replaced back into the bag.

So again, you can see our probabilities when we choose our second counter will remain the same, four sevenths pink and three sevenths blue.

So our outcomes now, if we follow the brunches of the tree diagram would be pink and then pink, pink and then blue, blue and then pink, and blue and then blue.

So that's what we call our outcomes for our probability tree diagram.

Let's have a look at this example, we told the probability of rain on Saturday is 0.

7.

And the probability of rain on Sunday is 0.

4.

And we've got to draw a probability tree diagram for the possible outcomes, for what happens on Saturday in terms rain and what happens on Sunday in terms of rain.

So I'm going to begin my tree diagram like this and label the probabilities of Saturday, it being raining or not raining.

So the two branches would lead onto rain and no rain.

And we can fill in the probability of it raining on Saturday as 0.

7 and following on for whatever happens on Saturday, we can say on Sunday, it's either going to rain or not rain.

And draw branches following on from there and label the probability of it raining on Sunday as 0.

4, we're told that information.

Similarly, if it doesn't rain on Saturday, we can then follow on on Sunday the probability of it raining on Sunday will remain as 0.

4.

Now we do have some probabilities missing from these branches, but the important thing to realise is that the probabilities must cover all the outcomes.

Which means that if it's going to rain with a probability of 0.

7, all the outcomes should add up to one.

So the probability of not raining would be 0.

3.

And similarly with the branches on Sunday, the probability of it raining is 0.

4, the probability therefore of it not raining must add up to one, so not raining must be 0.

6.

And similarly with the branch below on Sunday would be 0.

4 and 0.

6.

And we've got the outcomes listed there, got all the outcomes.

So on Saturday it could rain and then Sunday rains.

Similarly rain and then no rain, no rain and rain, no rain and no rain.

So those are all the probable outcomes.

Here's a question that you can try.

Pause the video to complete the task, resume the video once you're finished.

Here's the answer.

How did you get 'em? The important thing to remember with tree diagrams is that when you have a branch leading on to outcomes, those branches must always add up to one, whether they're fractions or decimals, make sure that your fractions or decimals add up to one.

Here's another question you can try.

Pause the video to complete the task, resume the video once you're finished.

Here are the answers.

So flipping a coin is a really good example of what an independent event is.

An independent event means that the outcomes that have happened previously don't impact the outcomes that will happen in the future.

Now, in this example, you're told about biassed coin.

And biassed just means that the probability lands itself towards one outcome or more than others.

So in this example, you are told that the probability that it lands on heads is 0.

4.

That means that the probability that it lands on tails must add up to one.

So it must be 0.

6.

In this question, you've got to draw the tree diagram for yourself, it's not drawn for you.

So pause the video to have a go, resume the video when you're finished.

In this question, you're not told the probabilities of the spinner landing on red or blue.

However, you are told that the spinner is fair and it's five sided.

So you can see from the diagram that there are three sections that are red and two sections that are blue.

So from that information, you can tell that the probability of the spinner landing on red would be three out of five, three fifths.

And the probability of it landing on blue would be two fifths.

Here's another question you can try.

Pause the video to complete the task, resume the video once you're finished.

Here's the answer for question four.

Now this question is very similar to an example earlier in the lesson.

So if you didn't quite get the answer to this, then maybe review the example earlier in the lesson.

Here's a question for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here's the answer.

This question's slightly different to the others that you've done so far, because there are three outcomes for this probability tree.

Alex's netball team could win, could draw or could lose.

So those are the three branches that you will need in your tree diagram.

The rules are the same, those three branches mut still add up to one.

I hope you've enjoyed this lesson as much as I have.

Thanks for watching.