Transcript Slide 1

General Probability Rules…
 If events A and B are
completely
independent of each
other (disjoint) then
the probability of A or
B happening is just:
P( A B)  P( A)  P(B)
P( A B)  P( A)  P(B)
We can extend the
rule
P( A B C)  P( A)  P(B)  P(C)
Probability Rules
 If events A and B are
independent of each
other (but not disjoint)
then the probability of
A and B happening
is just:
P( A B)  P( A)P(B)
Probability Rules
 If events A and B are
independent of each
other (but not disjoint)
then the probability of
A or B happening is
just:
P( A B)  P( A)  P(B)  P( A)P(B)
Hmmm – why is this “less” than the
disjoint case?
Examples…
 4.86
 4.89
 4.94
Conditional Probability
Sometimes, knowledge of an event alters
the probability of a future event. Example
4.30 illustrates this.
We write this as P(B|A), which
represents the probability of B
happening given the occurrence of A
Multiplication rules …
P( A and B)  P( A) P( B | A)
P( A and B)
P( B | A) 
P( A)
Examples…
4.101
4.103
Tree Diagrams…
 These are useful when there are a large number
of probabilities to consider
 Example: 38% of people earn a post secondary
degree. What is the probability of selecting a
person at random from a large crowd so that the
person is either female and has a PhD or male
with no post secondary degree? Use the data
from 4.94 and assume 50% of the general
population is male.
Plan of attack:
•Lay out all stems and branches
•Assign probabilities
•Calculate!
Decision Analysis…
This is a very useful application of stats!
Applications:
Medicine  course of treatment (example 4.37)
Computing Science  “fuzzy logic” and AI
Engineering/Business  production choices
What’s the best option?
In conclusion…
Make sure you understand what is meant
by conditional probability
Learn how to use (rather than memorize!)
the probability formulae
Ignore the sections on Baye’s Rule
Try 4.91, 4.92,4.97