A tree diagram is just a way of showing all the possible outcomes of an event or series of events. Above is an example of one showing the possible outcomes when you toss a coin twice:

There’s a few things you should know about them:

1) On any set of branches that meet at a point the probabilities must add up to 1

2) You multiply along branches to get the end outcome probabilities

3) The outcome probabilities should all add up to 1

4) If you need the probability of 2 outcomes you just add up their outcome probabilities**Example:** What is the probability you will toss a head then a tail, or a tail then a head:

P(head then tail or tail then head) = 1/4 + 1/4 = 0.5**NOTE:** Watch out for *conditional probability*. For example if you pick a card from a deck or a ball from a bag WITHOUT replacing your previous pick the probability changes.

So if you picked a card from a deck the probability of it being the ace of spades is 1/52….but if you did it a second time, not replacing the card you picked first, the probability would be 1/51.