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```General Mathematic
(HSC)
Tree Diagrams
Stage 6 - Year 12
Press Ctrl-A
©G Dear2009 – Not to be sold/Free to use
1
They should be used when multi-stage events occur.
They can be used to list the sample space.
Find the Sample Space for tossing three coins
Event 1 Event 2 Event 3
S={ HHH, HHT, HTH, HTT,
H 1
THH,THT,TTH, TTT }
H
T 2
H
H 3 Probability of only two tails
T
T 4
P(Only Two Tails) = 3
H 5
8
Number
of
H
T 6
T
elements
Probability
of three
7
H
T
sample space.1
T 8
P(HHH) =
8
n(S) = 8
Coin Toss
Button
2
The first event may effect the second event.
Four cards have the numbers 1 to 4 on them.
Draw a tree diagram to list all 2 digit numbers that
can be formed.
Event 1 Event 2
2
1
3
4
1
2
3
4
1
3
2
4
1
4
2
3
S={ 12,13,14,21,23,24,
31,32,34,41,42,43}
1 2
3 4
n(S) = 12
P(Even) = 6
12
=1
2
3
The first and second event may be different.
We can toss a coin and roll a dice.
Event 1 Event 2
1
2
3
H
4
5
6
1
2
3
T
4
5
6
S={ H1, H2, H3, H4, H5, H6,
T1, T2, T3, T4, T5, T6}
n(S) = 12
P(H,<4) = 3
12
=1
4
4
```