EE 2303

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Introduction to Probability
Keywords in Probability
Sample Problems in Probability
Overview of Experiment
Summary

What is Probability???
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Probability is a measure of “how likely an event is to happen”.
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Mathematical Expression:
Number of Favorable outcomes
Total Number of possible outcomes

Example
Tossing a coin:
Probability of getting an HEAD= ½
Probability of getting a TAIL=1/2

KEYWORDS IN PROBABILITY
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An experiment is any process that generates well-defined outcomes.
The sample space for an experiment is the set of all experimental outcomes.
An “Event” is an element of the sample space, any one particular outcome.

Tossing a Die
Events: Sample space:
3
4
5
1
2
6
Some graphic screen captures from
Seeing Statistics ®
Some images © 2001-(current year) www.arttoday.com
S ={1, 2, 3, 4, 5, 6}
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1
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6
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2
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4
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5
• 3
S

FACTS ABOUT PROBABILITY
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Permissible values for Probability: 0- 1
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Probability of an Impossible Event = 0
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Probability of Sure Event = 1
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Probability of Event not happening
= 1 – probability (event happening)
Probability (“Event happening at least once)
= 1- probability ( event not happening)

Sample Problems
Experiment: Rolling a die
Sample Space: S = {1, 2, 3, 4, 5, 6}
Probabilities: Each Event has a 1/6 chance of occurring.

Example
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Toss a fair coin twice. What is the probability of observing at least one head?
HH HT TH TT
ANSWER : Probability (at least 1 head) = 3/4
Some graphic screen captures from
Seeing Statistics ®
Some images © 2001-(current year) www.arttoday.com

Hints for Pre lab….
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When experiment is performed “n times”…
(Probability of event happening) n..
[note: for event to occur successively]
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Probability of Event not happening
= 1 – probability (event happening)
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Probability of Event happening at least once =
1- prob (event not happening)

Working in the Diagram
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Draw a For Loop
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Functions 
Structures  For
Loop
Draw a Case structure
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Functions 
Structures  Case

Adding More to Diagram
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Add a shift register
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Operate Value tool
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Right Click on edge of For Loop
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Select Add
Register
Add 2 addition boxes
Add division box

Adding More to Diagram
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Add Random
Number
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Functions 
Numeric 
Random (0-1)
Add Round to
Nearest
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Functions 
Numeric  Round to Nearest

Adding More to Diagram
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Add Equal box
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Functions 
Comparison 
Equal?
Add Wait box
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Functions  Time
& Delay  Wait
(ms)

Need Some Constants
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Add constant of value 100 to Wait
(ms)
Add constants of value 1 to
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Both additions
Shift Register
Add constant of value 0
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Equal box

Need Some Wire
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Wire the circuit up as shown
Change the case to “True”
Wire the tunnels through the Case structure
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Of “True” case

Run the Simulation
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Return to Front Panel
Change to Operate Value Tool
Choose a number of trials
“Run simulation once”

Summary
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Probability…
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Overview of Experiment..
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Hints to Pre lab…