 }
- 0 ≤ P(Ai) ≤ 1
Total probability of all possible outcomes within a set is 1, P(S) = 1
A1, A2, .. An are exhaustive if and only if P(A1 U A2 U .. An) = 1
3
Department of Risk and Disaster Reduction
UCL
Basic Probability rules (1)
If two events are independent
(i.e

P(B'IA')
B'
A'n B'
B
A'n B
9
Department of Risk and Disaster Reduction
UCL
Logic Trees Rules (1)
Events at the ends of different branches are mutually exclusive
1
B
1
P(BIĄ)
A
P(B'IA)
B
AnB
Start
P(A')
P(BIA')
A
P(B'IA')
B'
AnB
Events at the ends of different branches are mutually exclusive
P(A)
B
A'n B
A'n B
10
Department of Risk and Disaster Reduction
UCL
Logic Trees Rules (2)
Probabilities from an individual node sum to one
B
An B
P(BIA)
A
P(B'A)
B
P(A)
An B'
Start
I
1
P(A)
P(BIA')
A'
P(B'A')
B'
A'n B'
Probabilities from an individual node sum to one
Probabilities from an individual node sum to one
I
B
A'n B
11
Department of Risk and Disaster Reduction
UCL
Logic Trees Rules (3)
To calculate the probability of each event

, Uncertainty and Risk
Understanding probability is paramount for understanding and managing risk
Probabilistic approaches to risk assessment allow for decisions to be made based on models - it is important to remember models are by definition a simplification to reality
2Department of Risk and Disaster Reduction
UCL
Logic Trees
B
An B
P(BIA)
A
P(B'IA)
B
P(A)
An B'
Start
P(A')
P(BIA')
A'

P(B')
B'
A'n B'
B
A'n B
13
Department of Risk and Disaster Reduction
UCL
Logic Tree Example
Attenuation Equation 1
Soil depth 1
w3
Attenuation Equation 2
₩4 1-w3- w4
w2
Attenuation Equation 3
Soil type 1
Attenuation Equation 1
1-w2
Soil depth 2
w3
w1
w4 1-w3- w4
Attenuation Equation 2
Attenuation Equation 3
Attenuation Equation 1
w5
Attenuation Equation 2
w2
Attenuation Equation 3
Soil type 2
Attenuation
1-w2
Equation 1
w5
Soil depth 2
₩6
Attenuation Equation 2
1-w5-w6
Attenuation Equation 3
(1-w1)(1-w2)(₩6)
Characteristic Earthquake with estimated frequency 1-w1
Site Ground Motion
Soil depth 1
1w6 1-w5- w6Department of Risk and Disaster Reduction
UCL
Basic Probability
> The likelihood of an event occurring
A probability of 1 indicates absolute certainty
> A probability of 0 indicates there is no chance of that event occurring Set of possible outcomes

then the conditional probability of B given A is
· P(BIA) = P(An B) / P(A)
The multiplication law of probability:
· P(ANB) = P(A) P(B I A) and P(An B) = P(B) P(A I B)
Two events are independent if P(An B) = P(A) P(B)
8Department of Risk and Disaster Reduction
UCL
Integrating Science into Disaster Risk Reduction
Prof Joanna Faure Walker j.faure-walker@ucl.ac.uk
0
Department of Risk and Disaster Reduction
UCL
Probability - The Basics
Prof Joanna Faure Walker j.faure-walker@ucl.ac.uk
1
Department of Risk and Disaster Reduction
UCL
Probability

 Department of Risk and Disaster Reduction
UCL
Basic Probability Example 1
E.g consider throwing a normal dice once
· S={1,2,3,4,5,6}
 On the first throw P(1) = 16
· P(even) = P(2 or 4 or 6) = P(2) + P(4) + P(6) = 1/6 + 1/6 + 1/6 = 3/6 = 0.5
· P(not 5) = P(5') = 1 -P(5) = 1 - 6 = 5%
6
Department of Risk and Disaster Reduction
UCL
Basic Probability Example 2
E.g consider throwing an equally weighted coin twice,
· S={(H,H),(H,T), (T,H), (T,T)}
· The two throws are independent:
· On the first throw P(H) = 0.5, P(T) = 0.5, P(H or T) = 1

,one is not dependent on the other), the probability of both occurring:
· P(A1 and A2) = P(A1n A2) = P(A1)*P(A2)
(* means times)
Addition law for any two events: For two events A1 and A2, the probability of either occurring: U
P(A1 or A2) = P(A1 U A2) = P(A1) + P(A2) - P(A1 A2)
4
Department of Risk and Disaster Reduction
UCL
Basic Probability rules (2)
Addition law for mutually exclusive events:
If two events A1 and A2 are mutually exclusive, the probability of either occurring:
· P(A1 or A2) = P(A1 U A2) = P(A1) + P(A2)
This is derived from the addition law as if the two events are mutually exclusive, by definition, P(A1 A2) = 0
The probability of an event not occurring (the complement):
· P(not A1) = P(A1') = 1 - P(A1)
5

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