Probability tree diagrams
When more than one event takes place a tree diagram can be used to find all the possible outcomes.
This tree diagram shows all the possible outcomes and their probabilities for tossing a coin and for choosing a counter from a bag that has 3 red counters and 2 blue counters.
Notice that the outcomes are written at the end of each branch and the probabilities are written on each branch.
The four possible outcomes for these combined events are:
- head and a red
- head and a blue
- tail and a red
- tail and a blue
To calculate the probability of each event, multiply the probabilities along the relevant branches.
- \(P(HR) = 0.5 x 0.6 = 0.3\)
- \(P(HB) = 0.5 x 0.4 = 0.2\)
- \(P(TR) = 0.5 x 0.6 = 0.3\)
- \(P(TB) = 0.5 x 0.4 = 0.2\)