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