Subjective probability results from intuition

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Subjective probability  results from intuition, educated  guesses, and estimates.   Subjective Probability Example: A business analyst predicts that the probability of a  certain union going on strike is 0.15. Range of Probabilities Rule The probability of an event  E  is between 0 and 1,  inclusive.  That is   P(A)   1. Impossible to occur Certain to occur Even chance 0.5
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Complementary Events The  complement of Event  E   is the set of all outcomes  in the sample space that are not included in event E.  (Denoted  E   and read “E prime.”) P ( E ) +  P  ( E   )  = 1 Example:   There are 5 red chips, 4 blue chips, and 6 white chips in  a basket.  Find the probability of randomly selecting a  chip that is not blue. P ( E )   = 1 –  ( E   ( E   )  = 1 –  P ( E ) (selecting a blue chip)  4 0.267 15 = ( not  selecting a blue chip)  4 11 1 0.733 15 15 = - =
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Conditional Probability and the Multiplication Rule
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conditional probability   is the probability of an event  occurring, given that another event has already occurred. ( | A ) Conditional Probability “Probability of  B , given  A Example:   There are 5 red chip, 4 blue chips, and 6 white chips in a  basket.  Two chips are randomly selected.  Find the  probability that the second chip is red given that the  first chip is blue.  (Assume that the first chip is not  replaced.) (selecting a red chip|first chip is blue)  5 0.357 14 = Because the first chip is selected and not replaced,  there are only 14 chips remaining.
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Conditional Probability Less  then 5 5 to 10 More  than 10 Total Male 11 22 16 49 Female 13 24 14 51 Total 24 46 30 100 Example:   100 college students were surveyed and asked how many  hours a week they spent studying.  The results are in the  table below.  Find the probability that a student spends more  than 10 hours studying given that the student is a male. (more than 10 hours|male)  16 0.327 49 = The sample space consists of the 49 male students.  Of  these 49, 16 spend more than 10 hours a week studying.
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Two events are  independent   if the occurrence of one of  the events does not affect the probability of the other  event.  Two events  A  and  B  are independent if P  ( | A ) =  P  ( B ) or if  P  ( | B ) =  P  ( A ).  Events that are not independent are  dependent . Independent Events Example : Decide if the events are independent or dependent. Selecting a diamond from a standard deck of  cards ( A ), putting it back in the deck, and  then selecting a spade from the deck  (B ).
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