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More Fun With Probability Probability inherently is an abstract idea! In order to make Probability as concrete as possible, make a diagram or picture where applicable (i.e. Venn diagram, decision chart, tree diagram, 2 way table).

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General Addition Rules Same as Union or can be thought of as the probability of and/or.

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Example 1: 38% of RHS seniors take AP Econ, 12% of RHS seniors take AP Stats, while 8% take both. A) Find the probability that a senior takes AP Econ and/or (union with) AP Stats. b) Find the probability that a senior takes AP Econ but not AP Stats. Example 2: 82% of RHS seniors go to some form of college, while 8% go into the military directly after graduation. Assume college and military are disjoint, find the P(college U military).

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Conditional Probability Conditional probability that one event occurs given that another already has occurred. P(A|B) = P(AB) / P(B) P(AB) = Intersection of A and B = Probability of both A and B occurring at the same time.

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Example 3: Goals GradesPopularSports Boy Girl Find: a)P(Grades | Boy) b)P(Girl | Popular) c)P(Sports | Girl) d)P(Girl | Sports) e)P(Popular | Boy)

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Example 4: If you draw one card at random out of a regular deck of cards, find: a)P(ace | red) b)P(Queen | Face card) If you draw 2 cards consecutively at random out of a regular deck of cards, find: a) P( Queen | Jack of hearts) b) P( 3 | 3 of spades) c) P( heart | 2 of hearts)

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General Multiplication Rule (Intersection) P(AB) = P(B)P(A|B) If A and B are independent, then: P(B|A) = P(B) If P(AB) = 0, then the events are disjoint.

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Last Example! When an officer pulls over a potential DUI driver, 78% of officers give a breathalyzer test, 36% send the driver for a blood test, and 22% administer both. a)Make a diagram of the situation. Find the following: b) P( blood |breath) c)P(blood breath) d)P(breath | blood) e)P(No breath | blood) f)Are blood test and breathalyzer test disjoint? Explain. g)Are blood test and breathalyzer test independent? Explain.

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