# ch7 - Ch 7 Probability %and100 %minusthechanceof...

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1 Ch  7 Probability There are   3 definitions  of probability: Classical definition  is based on the assumption that the outcomes of an  experiment are  equally likely , e.g.  P (even number of rolling a die), P = number of favorable outcomes                 total number of possible outcomes Empirical definition  is based on  relative frequencies , e.g.  P (successful flights), P = number of times even occurred in the past            total number of observations Subjective definition  is based on an individual’s evaluation of available  opinions and other information, e.g.  P (getting an A in this course) Probabilities are between 0% and 100% The probability of something equals 100% minus the chance of  the opposite thing, i.e.  P(A)=100% - P(not A)   or  P(not A)=1-P(A)

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2 BOX A ( 3 Red, 2 Bl ue) Marbles of No. Total Marbles RED of No. Box B ( 30 Red, 20 Bl ue) One marble is drawn from a box: If it is  RED  you  win  Baht 100 If it is  BLUE  you  win  nothing Which box would you prefer?
3 Drawing WITH and WITHOUT  Replacement 1 2 3 1 2 1 2 3 W i t h Repl acement W i t hout Repl acement 2 DRAW 1DRAW I n DRAW 1 Car d no. 3 i s pi cked. The pr obabi l i t i es of DRAW 2 wi l l di f f er dependi ng on whet her :

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4 Question • One hundred tickets are drawn at random with  replacement from one of the two boxes below. On  each draw you will be paid the amount shown on the  ticket. Which box would you prefer and why? 1 2 1 3 a b
5 Expectations From the previous example,  We can calculate the  expected  payments as follows: For a) (50  ×  1) + (50  ×  2)=150  For b) (50  ×  1) + (50  ×  3)=200 And since a > b, we prefer b). 1 2 1 3 a b

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6 Conditional Probabilities • Assume you have a deck of cards • The top 2 cards are pulled out, and you will win  Baht 100 if the  second card  is a queen of hearts • You turn over the 1 st  card and it is a seven of clubs.  Now, what is your chance of winning? Conditional probability  is the probability of a  particular event occurring, given that another event  has occurred [i.e.,  P(A|B) ]
7 Question • Two tickets are drawn at random without replacement  from the following box • a) what is the chance that the second ticket is 4? • b) what is the chance that the second ticket is 4,  given  that the first is 2 ? 1 2 3 4

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8 Multiplication Rule • A box has 3 tickets  R, W, B • Two tickets are drawn WITHOUT replacement. What  is the chance of drawing an R then W? Soln 1)
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## This note was uploaded on 03/14/2010 for the course ECON Statistics taught by Professor Yy during the Spring '10 term at Seoul National.

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ch7 - Ch 7 Probability %and100 %minusthechanceof...

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