## Probability tree diagrams are just a picture..

.. that show all the possible outcomes from a series of events. They can be quite useful as probability needs some careful thought.

Watch the video and download the quick test – good luck!

This video deals with a GCSE question:

There are 3 strawberry yoghurts and 4 peach yoghurts in a fridge. Kate takes a yoghurt at random from the fridge. She eats the yoghurt. She then takes a second yoghurt at random from the fridge. Work out the probability that both yoghurts are the same flavour.

Click here for Quick Test Probability Tree Diagrams practice questions.

### Another example:

Imagine that Lauren is taking a bus to school. There are a couple of things to consider:

- Firstly, she is certain to be trying to take a bus. This means that there is a probability of 1, represented by a dot, on a probability tree
- She might catch, or miss, the bus

So the first part of a probability tree will look something like this:

2/3 of the time she catches and 1/3 of the time she misses. The 2/3 and 1/3 must add up to 1 as she is certain to be trying!

The next part of the probability tree deals with the next event:

- If Lauren catches the bus 3/4 of the time she’ll get to school before the bell, 1/4 of the time she’ll be late.
- Likewise, if Lauren misses the bus, and has to walk, 4 out of 5 times she’ll be late. 1/5 time she’ll make it.

Putting all this together a complete probability tree diagram will look something like this:

OK … so now lets look at ‘outcomes’ .. meaning the probability of an event happening. We multiply along the branches to work out the probability of each outcome.

Adding the different outcomes to each of the branches, Lauren’s probability tree should look something like this:

So the probability that Lauren misses the bus AND is late for school – outcome ML – is:

1/3 x 4/5 = 4/15

In other words for every 15 journeys Lauren will miss the bus and be late 4 times.

## Leave a Reply