Deductive versus Inductive Reasoning

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Basic Rules of Probability Objectives:  Determine if events are mutually exclusive.   Use probability rules to determine the probability of an event. Use a Venn diagram to determine probability of an event. Vocabulary:  mutually exclusive Probability Rules p(

p

 (S ) = ) 

p

(  )  

p

(E ) 

p

(

E

F

)  If events are mutually exclusive

p

(

E

F

) 

p

(

E

) 

p

(

E

 )  This formula can be rearranged as needed.

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Possible Classroom Examples: Determine if the following events mutually exclusive.?  E is the event of “being a doctor” and F is the event of “being a women”   E is the event of “being single” and F is the event of “being married” E is the event of “being a plumber” and F is the event of “being a stamp collector” Find the probability of each of the following:  a jack and a heart  a jack or a heart   not a jack of hearts above a jack    below a three both above a jack and below a three either above a jack or below a three  not a face card   If

o

(

E

above a five below a jack )  1 : 6 , the find

o

(E  ) Find the probability that the sum when a pair of dice is rolled is:  8 or 10  even and less than 5  even or less than 5 Alex is taking two courses, algebra and U. S. history. Student records indicate that the probability of passing algebra is .35, that of failing U. S. history is .35, and that of passing at least one of the two courses is .80. Find the probability that a. Alex will pass history b. Alex will pass both courses c. Alex will fail both courses d. Alex will pass exactly one course

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Deck of Cards Hearts – Red Diamonds – Red Clubs – Black Spades – Black Sum  Sum 2  (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) 2 3 4 5 6 10 11 12 7 8 9 10 11 12

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