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PROBABILITY

PROBABILITY. What is Probability?. Def : The chance of an event occuring. Where is it used? Lotteries, gambling, weather forecasting, insurance, investments, etc. Basic Concepts. Probability Experiment (or event) – A chance process that leads to well-defined results called outcomes .

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PROBABILITY

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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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