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Probability Calculus. Farrokh Alemi Ph.D . Probability Calculus. Co-occurring One of two occurring One occurring after another. What is probability?. Probability of A = . Joint & Marginal. One Two or more. Two Events Occurring. One or Other Event Occurring. - PowerPoint PPT Presentation
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PROBABILITY CALCULUSFarrokh Alemi Ph.D.
1. Co-occurring2. One of two occurring3. One occurring after
another
Probability Calculus
What is probability?
Probability of A =
OneTwo or more
Joint & Marginal
Two Events Occurring
One or Other Event Occurring
One or Other Event Occurring
HMO Market Penetration
HMO Market Penetration
Mutually Exclusive Outcomes
Mutually Exclusive Outcomes
=0
Addition Rule
Addition RuleP(A, B, …, or Z) = P(A)+P(B)+ … +
P(Z)
Do One: Computers Infected
Events Co-Occurring
Conditional Probabilities
Shrinking Universe of Possibilities
A
Shrinking Universe of Possibilities
A
Shrinking Universe of Possibilities
A
Shrinking Universe of Possibilities
A
Shrinking Universe of Possibilities
A
Shrinking Universe of Possibilities
A
Shrinking Universe of Possibilities
A
Shrinking Universe of Possibilities
A
Shrinking Universe of Possibilities
Shrinking Universe of Possibilities
Shrinking Universe of Possibilities
Hospitalization of Frail Patients
Multiplication Rule
Example of Multiplication Rule
P(Male & Frail) = P(Frail | Male) * P(Male)
Independence
P(B|A) = P(B)
Example
P(Jim|Joe) = P(Jim)
ExampleP(Jim|Joe)
not the same as P(Jim)
Multiplication Rule Simplified
Example
P(Joe & Jim) = P(Joe|Jim) × P(Jim)
P(Joe)
Conditional probability is calculated from reduced sample space
Take Home Lesson
1. Probability of getting a virus if computer has a spy?2. Probability of getting a spy, if computer has a virus?3. Probability of computers having both?4. Probability of infected computer?
Do one