Probability of Combined Events
Tree diagram
A branching diagram that lays out the outcomes and probabilities of combined events.
| English | Tree diagram |
|---|---|
| Bahasa Melayu | Gambar rajah pokok |
| 中文 | 树形图 |
How it is used
A box has 4 green and 6 yellow beads; two are drawn with replacement. A tree diagram shows two green branches (0.4 each), so P(both green) = 0.4 × 0.4 = 0.16 by multiplying along the top path.
Where it shows up in SPM
A key Paper 2 tool for combined events involving two or three stages, such as drawing beads or answering true/false items. You multiply along a path for 'and', then add the paths that meet the condition for 'or'.
Markers award method marks for a correctly labelled tree even before the final value.
Don't confuse it with
Open the chapter: Probability of Combined Events →
Frequently asked questions
Should the probabilities on each set of branches add up to something?
Yes. The branches coming out of any single point must add up to 1, because they cover all possibilities at that stage.
If your two branches read 0.4 and 0.6 that is correct; if they do not total 1 you have an error to fix before going further.
When do I multiply and when do I add on a tree diagram?
Multiply the probabilities as you move along one path from left to right, because that is a sequence of 'and' steps. Add the results of different complete paths when several paths each satisfy the required event, because that is an 'or' between separate ways it can happen.
Does 'with replacement' change how I label the second set of branches?
Yes. With replacement the item goes back, so the second branches use the same probabilities as the first.
Without replacement the total drops by one and the count of the drawn colour drops too, so the second branches must be relabelled with the new fractions.