1. Probability Tree Diagrams
GCSE Statistics
Probability
Tree Diagrams

2. A tree diagram can be used for combined events.
Each branch of the tree represents a possible combination of outcomes. The probability of the outcome is written on the branch.
For example, the tree diagram shows the outcome of drawing a ball from a bag containing five red and four green balls, noting it’s colour, replacing it and then drawing a ball and noting it’s colour.
ball 1
ball 2
outcome
probability
5 9 R RR
5 9 × 5 9 =
5 9 R
4 9
5 9 × 4 9 = G RG
5 9 R GR
4 9
4 9 × 5 9 = G
4 9
4 9 × 4 9 = G GG
Information can then be taken from the tree diagram

3. the total of these probabilities is 1G
5 9
4 9
ball 1
ball 2
outcome RR RG GR GG
probability
5 9 × 5 9 =
5 9 × 4 9 =
4 9 × 5 9 =
4 9 × 4 9 =
the total of these probabilities is 1
The probability of getting two balls the same colour
P(R and R) + P(G and G) = =
the probability of getting a red and a green ball would be:
P(R and G) + P(G and R) = =

4. 2 Independent Events. 3 Selections
For the higher tier exam you are expected to deal with tree diagrams that extend to 3 (or more) branches.
First Choice
Second Choice
Third Choice
red
2 Independent Events. 3 Selections
blue
red
red
red
blue
blue
red
red
blue
blue
blue
red
3 Ind/3 Select
blue

5. Sometimes one branch may finish earlier than others .
The tree diagram shows the probability of drawing a red ball from a bag of 3 black and 1 red ball. You win if you get the red ball.
Second Choice
1 4
3 4 R B
First Choice
1 4
3 4 R B
Third Choice
Outcome Probability
R = 1 4
BR = × 1 4 = 3 16
BBR = × × 1 4 = 9 64
BBB = × × 3 4 =
1 4
3 4 R B

6. Your turn
Exercise 7J page 278