tree diagram

A tree diagram is a way of showing every possible result from two or more events, and their probability.

We can place branches on the diagram to show the possibilities for each event.

Imagine that two bags contain balls of different colours. One bag contains 7 blue balls and 5 green balls, and the other bag contains 4 blue balls and 6 red balls. A ball is removed at random from the first bag and the colour is noted. Then, a ball is removed at random from the second bag and its colour is noted.

Opposite, the tree diagram has been completed.

We can see that the probability of removing two blue balls is:

\dfrac{7}{\text{12}} \times \dfrac{4}{10} = \dfrac{28}{120}