Draw and complete tree diagrams for independent and dependent events, with and without replacement, use 1 − P(none) for at least one, and (Higher) work out conditional probabilities and unknown numbers from a tree.
What you will learn
- Complete a tree diagram so each pair of branches adds up to 1
- Multiply along a route and add the routes you want
- Change the second branches when an item is not put back (Higher)
- Use 1 − P(none) for at least one
- Work out a probability given that something has happened, and solve for an unknown number of items (Higher)
Along the branches, then between them
Each pair of branches from one point adds up to 1.
To find the probability of one route, multiply along it. When several routes give what you want, add the routes.
- P(bus late) = 0.3 and P(train late) = 0.15, independent
- P(bus on time) = 1 − 0.3 = 0.7 and P(train on time) = 1 − 0.15 = 0.85
- late then on time: 0.3 × 0.85 = 0.255
- on time then late: 0.7 × 0.15 = 0.105
- P(exactly one late) = 0.255 + 0.105 = 0.36
A quick check: the four routes of a two-stage tree always add up to 1.
The rest of this lesson and its 10 practice questions are locked.
In this lesson
- Along the branches, then between them
- Without replacement, the second branches change (Higher)
- At least one
- Given that (Higher)
- Try it: First question
10 practice questions, marked as you go; about 30 minutes in all.
Key terms
Route, Add
In this unit: Probability and statistics: trees, experiments, samples and claims
More probability and statistics: tree diagrams in depth, expected outcomes from experiments, sampling and populations, critiquing charts and claims, and sample spaces in harder contexts.
- Tree diagrams in depth
- Expected outcomes and experiments
- Sampling and populations
- Critiquing charts and claims
- Sample spaces and combined events
All of Probability and statistics: trees, experiments, samples and claims