1. ©G Dear 2009 – Not to be sold/Free to use
Language
of Chance
General Mathematics
Preliminary
Tree Diagrams
Stage 6 - Year 11
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©G Dear 2009 – Not to be sold/Free to use

2. Tree Diagrams (1/3)
If there is more than one stage in a probability experiment we should use a tree diagram.
For Example: Tossing a coin twice.
Stage 1
Stage 2
Heads
Heads
Tails
S = {HH,
HT,
Heads
TH,
TT}
Tails
Tails

3. Tree Diagrams (2/3) For Example: Tossing a coin three times. Stage 1
Heads
HHH
Heads
Tails
HHT
Heads
Heads
HTH
Tails
Tails
HTT
n(s) = 8
Heads
THH
Heads
Tails
THT
Tails
Heads
TTH
Tails
Tails
TTT
S={
HHH,
HHT,
HTH,
HTT,
THH,
THT,
TTH,
TTT }

4. Tree Diagrams (3/3) For Example: Tossing a coin and a dice. Stage 1H1 2 H2
Heads 3 H3 4 H4 5 H5 6 H6
n(S) = 12 1 T1 2 T2
Tails 3 T3 4 T4 5 T5 6 T6
S={
T6}
H1,
H2,
H3,
H4,
H5,
H6,
T1,
T2,
T3,
T4,
T5,