Probability
Tree Diagrams

Learning Objective: I can use tree diagrams to calculate the
probability of combined events.
Standard: Calculate the probability of simple combined events, using
possibility diagrams and tree diagrams where appropriate (in possibility
diagrams outcomes will be represented by points on a grid and in tree
diagrams outcomes will be written at the end of branches and probabilities by
the side of the branches).
ACADEMIC VOCABULARY
 Probability A measure of how likely an event
is to happen
Tree diagrams for independent events
Two events A and B are independent if one
event happening has no effect on whether
or not the other event happens.
If A and B are independent, then
P(A happening and B happening) = P(A happening) × P(B happening)
P(A and B) = P(A) × P(B)
A bag contains four red marbles and two blue marbles.
Two marbles are chosen at random from the bag (with replacement).
Draw a tree diagram to show all the possible outcomes.
First choice
Second choice
4
6
4
6
2
6
R
Outcome
RR
Probability
4 4 16
 
6 6 36
R
2
6
B
RB
4 2 8
 
6 6 36
4
6
R
BR
2 4 8
 
6 6 36
BB
2 2 4
 
6 6 36
B
2
6
a Probability of two blues =
B
4
1

36
9
Multiply
along the
branches
A bag contains four red marbles and two blue marbles.
Two marbles are chosen at random from the bag (with replacement).
Draw a tree diagram to show all the possible outcomes.
First choice
Second choice
4
6
4
6
2
6
R
Outcome
RR
Probability
4 4 16
 
6 6 36
R
2
6
B
RB
4 2 8
 
6 6 36
4
6
R
BR
2 4 8
 
6 6 36
BB
2 2 4
 
6 6 36
B
2
6
B
b Probability of two the same colour = 16  4  20  5
36 36 36
9
A bag contains four red marbles and two blue marbles.
Two marbles are chosen at random from the bag (with replacement).
Draw a tree diagram to show all the possible outcomes.
First choice
Second choice
4
6
4
6
2
6
R
Outcome
RR
Probability
4 4 16
 
6 6 36
R
2
6
B
RB
4 2 8
 
6 6 36
4
6
R
BR
2 4 8
 
6 6 36
BB
2 2 4
 
6 6 36
B
2
6
c Probability of at least one red =
B
16 8
8
32
8




36 36 36 36
9
Tree diagrams for dependent events
Two events A and B are dependent if one
event happening has an effect on whether
or not the other event happens.
A bag contains four red marbles and two blue marbles.
Two marbles are chosen at random from the bag without
replacement. Draw a tree diagram to show all the possible outcomes.
First choice
Second choice
3
5
4
6
2
6
R
Outcome
RR
Probability
4 3 12
´ =
6 5 30
R
2
5
B
RB
4 2 8
´ =
6 5 30
4
5
R
BR
2 4 8
´ =
6 5 30
BB
2 1 2
´ =
6 5 30
B
1
5
a Probability of two reds =
B
12
2

30
5
Multiply
along the
branches
A bag contains four red marbles and two blue marbles.
Two marbles are chosen at random from the bag without
replacement. Draw a tree diagram to show all the possible outcomes.
First choice
Second choice
3
5
4
6
2
6
R
Outcome
RR
Probability
4 3 12
´ =
6 5 30
R
2
5
B
RB
4 2 8
´ =
6 5 30
4
5
R
BR
2 4 8
´ =
6 5 30
BB
2 1 2
´ =
6 5 30
B
1
5
B
b Probability of two different colours = 8  8  16  8
30 30 30 15
A bag contains four red marbles and two blue marbles.
Two marbles are chosen at random from the bag without
replacement. Draw a tree diagram to show all the possible outcomes.
First choice
Second choice
3
5
4
6
2
6
R
Outcome
RR
Probability
4 3 12
´ =
6 5 30
R
2
5
B
RB
4 2 8
´ =
6 5 30
4
5
R
BR
2 4 8
´ =
6 5 30
BB
2 1 2
´ =
6 5 30
B
1
5
B
c Probability of at least one blue =
8
8
2 18
3
+
+
=
=
30 30 30 30
5
IXL due BEFORE next class the
following week
Stage 8:
7th Grade DD.7 (at least 80%)
Stage 9:
8th Grade EE.7 (at least 80%)
IGCSE:
Algebra JJ.5 (at least 80%)