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More Fun With Probability

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). General Addition Rules.

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More Fun With Probability

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  1. 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).

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

  3. 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).

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

  5. Example 3: • Find: • P(Grades | Boy) • P(Girl | Popular) • P(Sports | Girl) • P(Girl | Sports) • P(Popular | Boy)

  6. Example 4: If you draw one card at random out of a regular deck of cards, find: • P(ace | red) • 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)

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

  8. 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. • Make a diagram of the situation. Find the following: b) P( blood |breath) • P(blood ∩ breath) • P(breath | blood) • P(No breath | blood) • Are blood test and breathalyzer test disjoint? Explain. • Are blood test and breathalyzer test independent? Explain.

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