Statistics 222 Exam 2

Statistics 222 Exam 2 - Statistics 222 Exam 2 Statistics...

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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 # of ways an event can occur/total # of possible outcome 0<probability then the event will not occur Probability is 1 or more then the event will occur Three methods to find probability o Theoretical is based on a theory Flipping coins In theory the coin is fair and both sides are equally likely to occur o Empirical is based on data o Personal based on individual’s judgment, and their own experiences Sample space is a list of all of outcomes A tree diagram is one method to create a sample space Combining probabilities o Assume that each branch of the tree diagram is independent o If you multiply probabilities across the tree then that gives the you the probability of a particular outcome o 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 Computing odds o A probability of x/y becomes x:y-x odds Probability of 1/6 becomes odds of 1:(6-1) = 1:5 o x:y x/(x+y) 1:5 1:6 Expected value (or average) o 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 o Expected value = expected winnings Ex: what are your expected winnings if you spent $1.00? Probability of loss is .999 with $0, probability of win is .001 with $500 0(.999)+500(.001)=.50 Similar to weighted average Combinations o The number of ways to choose r objects from a set of n objects without replacement and without regard to order o nCr=n!/r!(n-r)! o
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Statistics 222 Exam 2 - Statistics 222 Exam 2 Statistics...

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