Tree Diagrams
Objective: To calculate probability
using a tree diagram.
Five balls are put into a bag.
Three are red.
Two are blue.
A ball is chosen at random and replaced.
A second ball is then chosen.
Draw a tree diagram to show all the possible outcomes and their probabilities.
Lesley Hall @ Soar Valley College
Objective: To calculate probability
using a tree diagram.
Tree Diagrams
1st choice
R
3
5
You could either pick
out a red ball…
3
P(red ball) =
5
2
5
B
P(blue ball) =
… or a blue ball.
2
5
Lesley Hall @ Soar Valley College
Objective: To calculate probability
using a tree diagram.
Tree Diagrams
1st choice
2nd choice
R
3
5
2
5
R
B
R
B
B
Lesley Hall @ Soar Valley College
If you chose a red the 1st
time, you can still choose a
red or a blue the 2nd time.
If you chose a blue the 1st
time, you can still choose a
red or a blue the 2nd time.
Objective: To calculate probability
using a tree diagram.
Tree Diagrams
1st choice
3
5
2
5
2nd choice
R
B
3
5
R
2
5
B
3
5
R
2
5
B
Because we replace the first
ball the probabilities will
stay the same!
+
=1
Notice that on each pair of
branches the probabilities
add up to 1.
Lesley Hall @ Soar Valley College
Objective: To calculate probability
using a tree diagram.
Tree Diagrams
1st choice
3
5
2
5
2nd choice
R
B
3
5
R
2
5
B
3
5
R
2
5
B
List the outcomes …
Lesley Hall @ Soar Valley College
Objective: To calculate probability
using a tree diagram.
Tree Diagrams
1st choice
3
5
2
5
2nd choice
R
B
3
5
R
RR
9
3
3
+
=
25
5
5
2
5
B
RB
6
3
2
+
=
25
5
5
3
5
R
BR
6
2
3
+
=
25
5
5
2
5
B
BB
4
2
2
+
=
25
5
5
Finally check that
your
…and
work out the
probabilities add upprobabilities.
to 1.
Lesley Hall @ Soar Valley College
Objective: To calculate probability
using a tree diagram.
Tree Diagrams
1st choice
2nd choice
R
3
5
2
5
B
3
5
R
RR
9
3
3
+
=
25
5
5
2
5
B
RB
6
3
2
+
=
25
5
5
3
5
R
BR
6
2
3
+
=
25
5
5
2
5
B
BB
4
2
2
+
=
25
5
5
You can now use your tree diagram to answer questions.
Lesley Hall @ Soar Valley College