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Polling
Math1711Finite Math
Today's Goal:CalculatingProbability
set of all possible outcomesof an experiment
sample space
Uniform probability
maximum uncertaintymaximum fairnessmaximum entropy
+ Rule: Mutually exclusive events add:
× Rule: Independent events multiply:
a subset of the sample space
event
assigns a number in [0,1] tothe event E which measureshow likely the event is to occur
probability of the event
To comupte from counting ask yourself:
1) What is the sample space for the experiment?2) What is the event?3) How can I count them?
occurs when both events occur together
occurs when either or both events occur
occurs when E doesn't occur
Intersection
Union
Compliment
I roll two dice.Let E be the event that die 1 is even.Let F be the eventthat the dice sum to 6.
Compute
Compute
Compute
Inclusion Exclusion for Probability
Simpson's Paradox
Which kidney stone treatment is more effective?
Treatment A
Treatment B
Success
Total
Success
Total
Small Stone
81
87
234
270
Large Stone
192
263
55
80
Total
273
350
289
350
What does probability mean?
If I flip 100 coins, how many heads should I expect to see?
What's the probability I get exactly that many heads?
C. R. Charig, D. R. Webb, S. R. Payne, J. E. Wickham (29 March 1986). "Comparison of treatment of renal calculi by open surgery, percutaneous nephrolithotomy, and extracorporeal shockwave lithotripsy". Br Med J (Clin Res Ed) 292 (6524): 879–882. doi:10.1136/bmj.292.6524.879. PMC 1339981. PMID 3083922.