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Understanding Probability: Concepts, Rules, and Practical Examples

Dive into the abstract world of probability made concrete with visual aids like Venn diagrams and tree diagrams. Explore key concepts such as the General Addition Rules, Conditional Probability, and the General Multiplication Rule. Through real-world examples from high school seniors choosing courses to scenarios involving breathalyzer and blood tests during DUI stops, learn how to calculate probabilities effectively. Enhance your understanding of intersection and union of events, independence, and disjoint events, making probability both accessible and fun!

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Understanding Probability: Concepts, Rules, and Practical Examples

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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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