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Probability Calculus

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.

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Probability Calculus

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  1. Probability Calculus Farrokh Alemi Ph.D.

  2. Probability Calculus Co-occurring One of two occurring One occurring after another

  3. What is probability? Probability of A =

  4. Joint & Marginal One Two or more

  5. Two Events Occurring

  6. One or Other Event Occurring

  7. One or Other Event Occurring

  8. HMO Market Penetration

  9. HMO Market Penetration

  10. Mutually Exclusive Outcomes

  11. Mutually Exclusive Outcomes =0

  12. Addition Rule

  13. Addition Rule P(A, B, …, or Z) = P(A)+P(B)+ … + P(Z)

  14. Do One: Computers Infected

  15. Events Co-Occurring

  16. Conditional Probabilities

  17. Shrinking Universe of Possibilities A

  18. Shrinking Universe of Possibilities A

  19. Shrinking Universe of Possibilities A

  20. Shrinking Universe of Possibilities A

  21. Shrinking Universe of Possibilities A

  22. Shrinking Universe of Possibilities A

  23. Shrinking Universe of Possibilities A

  24. Shrinking Universe of Possibilities A

  25. Shrinking Universe of Possibilities

  26. Shrinking Universe of Possibilities

  27. Shrinking Universe of Possibilities

  28. Hospitalization of Frail Patients

  29. Multiplication Rule

  30. Example of Multiplication Rule P(Male & Frail) = P(Frail | Male) * P(Male)

  31. Independence P(B|A) = P(B)

  32. Example P(Jim|Joe) = P(Jim)

  33. Example P(Jim|Joe) not the same as P(Jim)

  34. Multiplication Rule Simplified

  35. Example P(Joe) P(Joe & Jim) = P(Joe|Jim) × P(Jim)

  36. Take Home Lesson Conditional probability is calculated from reduced sample space

  37. Do one 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?

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