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.