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Chapter 4 – Probability and Counting Rules Section 4.1 – Sample Spaces and Probability

Chapter 4 – Probability and Counting Rules Section 4.1 – Sample Spaces and Probability. Probability. Three basic interpretations of probability Classical – (use theory to find) I am not likely to win the Cash 3 today. Emperical – (use experiments to find) there is a 40% chance of rain.

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Chapter 4 – Probability and Counting Rules Section 4.1 – Sample Spaces and Probability

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  1. Chapter 4 – Probability and Counting RulesSection 4.1 – Sample Spaces and Probability

  2. Probability Three basic interpretations of probability • Classical – (use theory to find) • I am not likely to win the Cash 3 today. • Emperical – (use experiments to find) • there is a 40% chance of rain. • Subjective – (use personal judgment to find) • USC has a 40% chance of beating Clemson this season.

  3. Probability • Probability Experiment: • a chance process that leads to well-defined results called outcomes. • Outcome: • the result of a single trial of a probability experiment. • Sample Space: • the set of all possible outcomes of a probability experiment.

  4. Sample Space

  5. Sample Space • What is the sample space for the gender of the children if a family has 1 child? • B G • What about 2 children? • BB BG GB GG • 3 children? Try this in your notes… • BBB BBG BGB BGG GBB GGB GBG GGG • this can become pretty difficult. • a tree diagram can help…

  6. Sample Space • Tree diagram • a device consisting of line segments emanating from a starting point and also from the outcome point. • It is used to determine all possible outcomes of a probability experiment. • Now, make one for 3 children…… • Try making one for flipping 2 coins… • Now, try flipping a coin, then rolling a die…

  7. Probability • Event: • a set of outcomes of a probability experiment. • can be one or more outcomes. • if a die is rolled, the number that comes up is the outcome • An event with one outcome is called a simple event. • Several outcomes make a compound event. • simple event  rolling a 4 on a die. • compound event  rolling an even number on a die.

  8. Classical Probability • Equally Likely Events are events that have the same probability of occurring. • Rounding Rules – • probabilities should be expressed as reduced fractions or rounded to 2 or 3 decimal places. • with very small probabilities, round to the first nonzero digit • ex. 0.000000496  0.0000005

  9. Complementary Events • Complement of an event E : • the set of outcomes in the sample space that are not included in the outcome of the event E. The complement is E-bar. What is the complement of • rolling a die and getting a 2? • drawing a diamond out of a deck? • flipping two coins and getting two heads? • selecting a day of the week and getting a weekday? • selecting a month and getting a month that begins with J?

  10. Complementary Events RULES FOR COMPLEMENTARY EVENTS:

  11. Empirical Probability • Empirical Probability relies on actual experience to determine probabilities. • experiments • observations • Instead of using theory, we will try things out • flipping a coin 500 times and counting the heads. • how many should we expect?

  12. Empirical Probability Formula for Empirical Probability • In a sample of 50 people, 21 had type O blood, 22 had type A blood, 5 had type B blood, and 2 had type AB blood. • Set up a frequency distribution for this data • find the following probabilities: • P (type O) = • P (type A) = • P (not AB) =

  13. Subjective Probability • Subjective Probability is based on an educated guess. • 70% chance Tiger Woods will win the next tournament. • 30% chance a patient will need an operation.

  14. Practice • page 196 #11 in your notes… • now try 12 in your notes… • assignment: • p 196 # 1 – 29 odd

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