1. Lecture 1
Sec

2. Outline
Define terms with an example (outcome, sample space, event, an event space)
Axioms of probability

3. Ficticious Experiment
Experiment: flip a coin three times. Observe the sequence of heads and tails.
Question: Assuming that the coin is fair, what is the maximum number of heads and tails?

4. Ficticious Experiment
Experiment: flip a coin three times. Observe the sequence of heads and tails.
Results:
hhh
hht
hth
htt
thh
tht
tth
ttt
outcome
sample space
Definition of an outcome: any possible observation of
the experiment
Sample space: a set of all possible outcomes.

5. Another Example

6. Ficticious Experiment
Procedure: flip a coin three times. Observe the sequence of heads and tails.
Results:
hhh
hht
hth
htt
thh
tht
tth
ttt
An event is a set of outcomes with the first flip
being a head.

7. Exercise
What are the outcomes associated with each event?

8. Event A and event B
Event A and event B are mutually exclusive.

9. Event C and Event D Event D Event C
Event C and D are not mutually exclusive!

10. Exercise
What are the probabilities for event A, B, C and D?

11. Notation x In Set theory, a set is a collection of things. B is a set.
A is a subset of B, i.e. A⊂𝐵
A subset can also be empty. A null set, an empty set has no element.
The notation of a null is 𝜙.

12. Intersection
The intersection of two sets C and D is the set of all elements which are contained in both C and D.
Event D
Event C
𝐶∩𝐷

13. Union
The union of sets C and D is the set of all elements that are either in C or in D, or in both.
C ∪𝐷

14. Mutually Exclusive
𝐴∩𝐵=𝜙

15. Quiz
Monitor three consecutive phone calls going through a telephone switching office. Class each one as a voice call (v) if someone is speaking, or a data (d) if the call is carrying a modem or fax signal. Your observation is a sequence of three letters each letter is either v or d.
Write down the following events:
First call is a voice call
One or more voice call

16. Answer Write down the following events: First call is a voice call
A1={vvv,vvd,vdv,vdd}
One or more voice call
A4={vvv,vvd,vdv,dvv,vdd,dvd,ddv}

17. Telephone Usage What is the sample space?
What is the probability of the sample space?

18. Telephone Usage
What is the probability associated with the long call?

19. Telephone Usage What is the probability associated with the brief call
if you know the probability of a long call?