1 / 5

Conditional Probability Warm-Up

Conditional Probability Warm-Up. Remember how to estimate how many people answer yes to embarrassing question P. Calculating Pr(P ) from Pr(H∪P ). H. P. Because H and P are independent events, Pr(H∩P ) = Pr(H ) ∙ Pr(P ). Pr(H ) = .5 Pr(H∪P ) = Pr(H ) + Pr(P ) - Pr(H∩P ).

aric
Download Presentation

Conditional Probability Warm-Up

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Conditional Probability Warm-Up Remember how to estimate how many people answer yes to embarrassing question P

  2. Calculating Pr(P) from Pr(H∪P) H P Because H and P are independent events, Pr(H∩P) = Pr(H) ∙ Pr(P). Pr(H) = .5 Pr(H∪P) = Pr(H) + Pr(P) - Pr(H∩P). So Pr(P) = Pr(H∪P) - Pr(H) + Pr(H)∙Pr(P) Pr(P) = Pr(H∪P) -.5 + .5 ∙ Pr(P) Pr(P) = 2 ∙ Pr(H∪P) – 1

  3. Now Suppose You Raise Your Hand:How Suspicious Should I Be of You? That is, what is Pr(P | H∪P)? Let R = H∪P, r = Pr(R), p = Pr(P) = 2r-1 We want Pr(P | R) = Pr(P∩R)/Pr(R) But P∩R = P∩(H∪P) = P So Pr(P∩R)/Pr(R) = Pr(P)/Pr(R) = p/r = (2r-1)/r = 2 – 1/r If r = ¾, Pr(P|R) = 2 – 4/3 = 2/3

  4. Important Lessons! So if r = .5, Pr(P|R) = 0; if r = 1, Pr(P|R) = 1 With only a finite sample, impossible to calculate probabilitiesprecisely

  5. FINIS

More Related