Lesson video

Hi, my name's Mr. Chan.

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

Let's begin with this example.

A bag contains four pink and three blue counters.

We can see that in the diagram.

A counter is chosen at random and not replaced.

Then another counter is chosen at random.

Draw a probability tree diagram for the possible outcomes.

So we're picking out counters twice.

So we can say that we've got first pick and second pick, and we can only pick out blue and pink counters, and we can begin our tree diagram like this.

So we can see from the diagram all the information given that we have four pink counters out of the total number of seven.

So the probability would be 4/7, and the blue it would be 3/7 'cause we've got three out of a total possible number of seven.

Now in our second pick, we can see, we can only pick out pink and blue counters again.

However, what happens if we've picked out a pink counter first? We're told that that's not replaced.

So that changes the probabilities in our second pick.

And this is why this is called dependent event.

It depends on what happens in the first pick or the first situation.

We also call this conditional probability because the probability is on the condition of what happens.

So in this situation, we've picked out a pink one.

Look at what's left in the bag.

We only have three pink left out of total possible six now.

So the probability of picking pink would be 3/6, and we have three blue out of six in the bag, so that would be 3/6 for blue as well.

So what happens if a blue one was picked out first of all? So we can see the blue ones being picked out.

Look at what's happened in the situation of the counters in the bag.

We now have four pink counters out of a total possible of six.

So that would be our probability there.

And because we've picked out a blue counter to start with, we have one less blue counter and one less counter altogether.

So we would have a probability of two out of six there.

So that's my tree diagram, and the possible outcomes are listed there pink and then pink, pink and then blue, blue and then pink, and finally blue and then blue.

Let's look at another example.

We've got a bag containing seven red and five green sweets.

We're told that Tommy eats two of the sweets at random.

Draw a probability tree diagram for the possible outcomes.

So I'm going to just draw a representation of our bag of sweets.

I've got seven red and five green sweets there.

So Tommy is going to pick out two sweets at random and he can only pick out red and green sweets.

So our tree diagram is going to begin like this.

So in our first pick, Tommy can have a chance of picking out seven out of a total possible 12 red sweets there.

So that would be 7/12.

And there are five green sweets out of a total 12 again.

So the probability of Tommy picking out a green sweet would be 5/12.

In our second pick, he can again only pick out red and green sweets.

Now, again, what happens if he has picked out a red sweet to start with? So he eats that and then it's not replaced.

So what we can say now is what has happened to the number of red sweets, there's one less and there's one less in total number of sweets.

So there were seven red, he's eaten that red one now, so now there are six red and there's one less sweet altogether.

So we now have six out of 11 in terms of the probability of his second pick being a red sweet.

There are still five green sweets, but one less in total, so the probability of green would be 5/11.

So let's consider what happens if he had picked out a green sweet to start with.

He's eaten that, so look what's happened to the number of red sweets.

That has remained the same so it's still seven, but there's one less sweet altogether, 7/11.

And in terms of if he has picked out a green sweet there's one less green, but there are still the same number of red, but there's one less altogether.

So we have one less green sweet which makes 4/11.

So the probability tree diagram is shown there, and the possible outcomes as you can see, are listed there.

Red and then red, red and then green, green and then red, and finally green and then green.

Here's a question for you to try.

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

Here are the answers.

These events are called dependent events because the probabilities depend on what's happened previously, and they do impact on what happens in the future.

So in this question, you have Jack taking a sweet depending on whether it's a red sweet or a blue sweet, that changes the probability in the second branch of your tree diagram.

So have a look at what's happened there and hopefully you've got the correct answers.

Here's another question for you to try.

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

Here's the answer.

In this question we're told that Amir has a bag with four green and three blue counters.

He takes a counter and doesn't replace it.

Now that's a big clue to tell you that because he doesn't replace the counter, that this is a dependent event which leads to conditional probabilities, because what happens in the first pick that he takes a counter from the bag, that will impact on what happens in the second pick because that means he's got one less of the colour that he's picked out to start with.

Here's another question for you to try.

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

Here's the answer.

I hope by now you're getting to grips with drawing these tree diagrams where there're dependent events.

In this question, we're told that Rosie takes a piece of fruits and then she eats it, which means she doesn't replace that piece of fruit.

So that leads to a dependent event for the second time that Rosie picks a piece of fruit from the bag.

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.

So if Paul takes two pens out of his pencil case, he started with eight, so if he took out a red pen to start with that means he would have one less red pen, but one less pen in total in the pencil case.

Similarly, if he took out a blue pen to start with, he would have one less blue pen, but also one less pen in total in the pencil case.

So hopefully you've got the correct answer there.

That's all for this lesson, thanks for watching.