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Understanding Probability Concepts: A Comprehensive Guide

Explore the fundamental concepts of probability, from probability experiments to sample space and rules of probability calculation. Discover how probability is applied in various fields like gambling, weather forecasting, investments, and more.

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Understanding Probability Concepts: A Comprehensive Guide

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  1. PROBABILITY

  2. What is Probability? • Def: The chance of an event occuring. • Where is it used? • Lotteries, gambling, weather forecasting, insurance, investments, etc.

  3. Basic Concepts • Probability Experiment (or event) – A chance process that leads to well-defined results called outcomes. • Examples: tossing a coin, rolling a die, drawing a card from a deck, etc.

  4. Basic Concepts • Outcome – The result of a single trial of a probability experiment • Examples: Getting Heads when tossing a coin Getting a 6 when rolling a die Getting a Queen when choosing a single card from a deck of cards

  5. Basic Concepts • Sample Space – The set of all possible outcomes of a probability experiment. • Examples:

  6. Basic Concepts • An event can have a single outcome (simple event) or more than one outcome (compound event). • Simple event – tossing a single die • Compound event – tossing a pair of dice.

  7. Classical Probability • Assumes that all outcomes in the sample space are equally likely to occur. • Formula: The probability of event E occuring is given by:

  8. Example 1 : • For a card drawn from an ordinary deck, find the probability of getting a queen.

  9. Example 2: • A roulette wheel has 38 spaces numbered 1 through 36, 0 and 00. Find the probability of getting these results. • An odd number • A number greater than 25. • A number less than 15 not counting 0 and 00.

  10. Example 2: Solution • Sample Space = {0, 00, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}

  11. Example 3: • A card is drawn from an ordinary deck of cards. Find these probabilities: • Of getting a jack. • Of getting the 6 of clubs. • Of getting a 3 or a diamond. • Of getting a 3 and a diamond.

  12. Basic Rules of Probability • The probability of an event occuring cannot be greater than 1 or less than 0. (same as 0 to 100%) • Probability can be expressed as a fraction, decimal or percent. • The probabilities of all events in a sample space will always sum to 1. (100%) • The probability of an event occuring will always be the same as 1 – the probability or the event not occuring. (Complement Rule)

  13. The Complement Rule • P(E) = 1 – P’(E) • Example: In a survey 36% of American parents use bribery to get their children to behave. If a parent is selected at random, what is the probability he/she does not use bribery? • P(does not use) = 1 – P(uses) • P(does not use) = 1 - .36 = .64 or 64%

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