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Lecture2_Chap2Pt2

# Lecture2_Chap2Pt2 - Probability Countingand Independence...

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Probability Counting and  Independence

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Review Up until now we have been given  probabilities.  Then, based on these  probabilities, we’ve used the axioms of  probabilities, along with supplementary  rules, to figure out other probabilities.
Example 50% of all shoppers at a certain pet  store own cats.  30% of all customers  own dogs.  40% of all customers own  neither a cat or a dog.  What percent of shoppers own a cat,  but not a dog?  What percent own both  a cat and a dog?

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How to determine probabilities Longterm Relative Frequency Counting equally probable outcomes
Longterm Relative Frequency To find the probability of a certain  outcome we can look at the proportion  of times it occurs if we perform a LOT of  experiments.

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Examples Getting 50121 heads while flipping a  quarter 100,000 times indicates the  probability of getting heads is close to  50% If we roll a fair die 600,000 times we  expect to get the number one about  100,000 times.
Limitations Some types of experiments cannot  feasibly be repeated over and over and  over.  For instance, launching space  shuttles or missile defense systems.    Or looking at the longterm effects of  interest rate changes.

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Equally Probable Outcomes Assume that an experiment has N  equally  probable simple events.  That  is, the number of elements in the  sample space, S, is N. The probability of any compound event  A, P(A) can be found by n/N, where n is  the number of simple outcomes that  make up A.
Example Let A be the event of getting 3 of a  kind in a 5 card poker hand.   P(A) = (Number of ways to get 3 of a  kind on a five card hand) / (Total  number of possible five card hands)

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Example continued This means that be able to compute  probabilities we need to be able to  figure out how to count the total number  of ways something can occur.
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Lecture2_Chap2Pt2 - Probability Countingand Independence...

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