Tree diagrams are useful to answer probability questions where there is more than one event happening in succession.

Look at this example, which shows the probability that my bus is on time or late on Monday and Tuesday.

The probability that it is on time on any day is 0.7 and the probability that it is late is 0.3.

To work out the probability that it will be late on Monday and on Tuesday, we travel down the relevant route and **multiply **the probabilities together.

P(late on two days) = 0.3 x 0.3 = **0.09**

__Example__

What is the probability that my bus will be late on only one of the days?

**Answer**

There are two options here, clearly visible on the tree diagram and shown in red below.

P(late on Monday only) = 0.3 x 0.7 = 0.21

P(late on Tuesday only) = 0.7 x 0.3 = 0.21

We must now **add **these two probabilities, because either option is relevant.

P(late on one day only) = 0.21 + 0.21 = **0.42**