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Polling
Math1711Finite Math
Today's Goal:Probability
set of all possible outcomesof an experiment
sample space
Experiment: Roll a die.
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
What is the sample space?
What set represents theevent of an even number?
How do we compute theprobability of an event?
What's the probability of beingdealt a royal flush in spaces?
Quiz: Buzz rolls a 6-sided diethen draws that many cards.How many possible sets of cardscan Buzz obtain?
Buzz rolls a 6-sided diethen draws that many cards.What is the probability thatBuzz drew the Queen of Hearts?
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
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?