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Understanding General Probability Rules and Conditional Probability Applications

This section covers the fundamental rules of probability, including the General Addition Rule, Multiplication Rule, and Conditional Probability. It provides practical examples such as calculating the probability of drawing a red marble from selected urns and evaluating probabilities related to defective switches in a model railroad circuit. Additionally, it discusses selecting utility patents and determining their probabilities based on various conditions, such as foreign or US patents. This comprehensive overview aims to clarify key concepts and techniques in probability.

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Understanding General Probability Rules and Conditional Probability Applications

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Presentation Transcript

  1. More on Probability (Text Sec. 6.3) General Probability Rules

  2. See Sec. 6.3 Summary for Recap of Definitions and Rules/Formulas. • Key Notes • General Addition Rule • Multiplication Rule • Conditional Probability

  3. Urn 1 Contains 5 red marbles and 3 black marbles. Urn 2 contains 3 red marbles and 1 black marble. Urn 3 contains 4 red marbles and 2 black marbles. If an urn is selected at random and a marble is drawn, find the probability it will be red.

  4. Conditional Probability Example • A circuit to run a model railroad has 8 switches. Two of them are defective. If a person selects two switches at random and test them, find each probability: • Both are good. • Both are defective. • The first is defective and the second is good. • The second is good, given the first is good. • The second is defective, given the first is defective.

  5. Consider the following table concerning utility patents granted for a specific year. • If a patent is selected at random, find the probability that the patent is… • Foreign • A US patent or Individual • A Foreign patent, given it was issued to a corporation • Issued to a Corporation, given it was a US patent • A Government patent, given it was issued in a Foreign country.

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