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Statistics and Lottery
Probability: the proportion of times the vent is expected to occur when the experiment is
repeated under identical conditions
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# of ways an event can occur/total # of possible outcome
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0<probability then the event will not occur
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Probability is 1 or more then the event will occur
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Three methods to find probability
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Theoretical is based on a theory
Flipping coins
In theory the coin is fair and both sides are equally likely to occur
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Empirical is based on data
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Personal based on individual’s judgment, and their own experiences
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Sample space is a list of all of outcomes
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A tree diagram is one method to create a sample space
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Combining probabilities
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Assume that each branch of the tree diagram is independent
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If you multiply probabilities across the tree then that gives the you the
probability of a particular outcome
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If you multiply the probabilities across the three and then add the
probabilities up and down the three then you get the probability
involving several outcomes
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Computing odds
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A probability of x/y becomes x:yx odds
Probability of 1/6 becomes odds of 1:(61) = 1:5
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x:y
x/(x+y)
1:5
1:6
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Expected value (or average)
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The expected value of a random phenomenon that has numerical
outcomes is found by multiplying each outcome by its probability and
then summing over all possible outcomes
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Expected value = expected winnings
Ex: what are your expected winnings if you spent $1.00?
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Probability of loss is .999 with $0, probability of win is .001
with $500
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0(.999)+500(.001)=.50
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Similar to weighted average
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Combinations
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The number of ways to choose r objects from a set of n objects without
replacement and without regard to order
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nCr=n!/r!(nr)!
o
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 Fall '10
 ROSEMARTINEZDAWSON

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