Lecture15Sept08

Lecture15Sept08 - Computing Complicated Probabilities Sept....

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Computing Complicated Probabilities Sept. 2008
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We have now seen some of the most important equations for combining probabilities If A and B are events P(AUB)=P(A)+P(B)-P(A∩B) If P(B)>0 P(A∩B)=P(A|B)P(B) and if A and B are independent P(A∩B)=P(A)P(B)
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A Common Probability Fallacy is treating conditional events as if they are independent along with ignoring co-occurring events that affect the probabilities
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Coincidence When someone wins a 2 nd large prize in the lottery, it makes the headline news. What is the probability that this will happen? If we assume, e.g. that 1 million tickets were sold each time and that the draws were independent, the probability that a person purchases 1 ticket in each lottery and that ticket wins both is 10 -6 x 10 -6 which is a very small number (and is the type of computation you usually find in the accompanying article). What is wrong with this?
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When someone wins a 2 nd large prize in the lottery, it makes the headline news. What is the probability that this will happen? If we assume, e.g. that 1 million tickets were sold each time and that the draws were independent, the probability that a person purchases 1 ticket in each lottery and that ticket wins both is 10 -6 x 10 -6 which is a very small number (and is the type of computation you usually find in the accompanying article). What is wrong with this? Firstly, in each lottery, although each ticket has probability 10 -6 of being drawn, the probability that someone will win is 100%. Secondly, there are many lotteries going on, many of which have several large prizes. There are a lot of people who purchase multiple tickets on multiple lotteries. The articles never report the numbers of tickets the multiple winners have actually purchased over a lifetime. In short, the independence computation is wrong.
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Lecture15Sept08 - Computing Complicated Probabilities Sept....

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