Probability-Tree-Diagrams Aqa Foundation

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Exam code:8300

Tree diagrams

How do I draw a tree diagram?

Tree diagrams can be used for repeated experiments with two outcomes
- The 1st experiment has outcome A or not A
- The 2nd experiment has outcome B or not B
Read the tree diagram from left to right along its branches
- For example, the top branches give A followed by B
  - This is called A and B

How to set up a tree diagram for two experiments each with two possible outcomes

How do I find probabilities from tree diagrams?

Write the probabilities on each branch
- Remember that P(not A) = 1 – P(A)
  - Probabilities on each pair of branches add to 1
Multiply along the branches from left to right
- This gives P(1st outcome and 2nd outcome)
Add between the separate cases
- For example
  - P(AA or BB) = P(AA) + P(BB)
The probabilities of all possible cases add to 1
If asked to find the probability of at least one outcome, it is quicker to do 1 – P(none)

Examiner Tips and Tricks

When multiplying along branches with fractions, don’t cancel fractions in your working – having the same denominator makes them easier to add together!

Worked Example

A worker drives through two sets of traffic lights on their way to work.
Each set of traffic lights has only two options: green or red.
The probability of the first set of traffic lights being on green is $5 over 7$ .
The probability of the second set of traffic lights being on green is $8 over 9$ .

(a) Draw and label a tree diagram. Show the probabilities of every possible outcome.

Work out the probabilities of each set of traffic lights being on red, R
Use P(red) = 1 – P(green)

$straight P open parentheses 1 to the power of st space straight R close parentheses equals 1 minus straight P open parentheses 1 to the power of st space straight G close parentheses equals 1 minus 5 over 7 equals 2 over 7$
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Maths Gcse Aqa Foundation