How can you work out the probability of two events happening using a tree diagram?

We multiply the probabilities of those events

happening.

If for example we are given the following probabilities:

In Basket 1, P(Apple) = 0.25 and P(Pear) = 0.75

In Basket 2, P(Apple) = 0.65 and P(Pear) = 0.35

The probability of picking an apple from Basket 1 and a pear from basket 2 would be = 0.25*0.35

You multiply probabilities when you move across a tree diagram branch and add probabilities when moving up and down the branches. Conditional probabilities work slightly different. You will need to engage Bayes's theorem

Multiply across the branches of the sequence you require

A probability tree indicates probabilities and some conditional probabilities for combinations of events. 

Example: Flipping a biased coin twice. 

Event 1- first coin flip; Event 2- second coin flip