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Chapter 11

Chapter 11. Probability. Chapter 11: Probability. 11.1 Basic Concepts 11.2 Events Involving “Not” and “Or” 11.3 Conditional Probability and Events Involving “And” 11.4 Binomial Probability 11.5 Expected Value and Simulation. Section 11-2. Events Involving “Not” and “Or”.

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Chapter 11

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  1. Chapter 11 Probability

  2. Chapter 11: Probability • 11.1 Basic Concepts • 11.2 Events Involving “Not” and “Or” • 11.3 Conditional Probability and Events Involving “And” • 11.4 Binomial Probability • 11.5 Expected Value and Simulation

  3. Section 11-2 • Events Involving “Not” and “Or”

  4. Events Involving “Not” and “Or” • Know that the probability of an event is a real number between 0 and 1, inclusive of both, and know the meanings of the terms impossible event and certain event. • Understand the correspondences among set theory, logic, and arithmetic. • Determine the probability of “not E” given the probability of E. • Determine the probability of “A or B” given the probabilities of A, B, and A and B.

  5. Properties of Probability Let E be an event from the sample space S. That is, E is a subset of S. Then the following properties hold. (The probability of an event is between 0 and 1, inclusive.) (The probability of an impossible event is 0.) (The probability of a certain event is 1.)

  6. Example: Finding Probability When Rolling a Die When a single fair die is rolled, find the probability of each event. a) the number 3 is rolled b) a number other than 3 is rolled c) the number 7 is rolled d) a number less than 7 is rolled

  7. Example: Finding Probability When Rolling a Die Solution There are six possible outcomes for the die: {1, 2, 3, 4, 5, 6}. a) the number 3 is rolled b) a number other than 3 is rolled c) the number 7 is rolled d) a number less than 7 is rolled

  8. Events Involving “Not” The table on the next slide shows the correspondences that are the basis for the probability rules developed in this section. For example, the probability of an event not happening involves the complement and subtraction.

  9. Correspondences

  10. Probability of a Complement The probability that an event E will not occur is equal to one minus the probability that it will occur. E S So we have and

  11. Example: Finding the Probability from a Complement When a single card is drawn from a standard 52-card deck, what is the probability that it will not be an ace? Solution

  12. Events Involving “Or” Probability of one event or another should involve the union and addition.

  13. Mutually Exclusive Events Two events A and B are mutually exclusive events if they have no outcomes in common. (Mutually exclusive events cannot occur simultaneously.)

  14. Addition Rule of Probability (for A or B) If A and B are any two events, then If A and B are mutually exclusive, then

  15. Example: Finding the Probability of an Event Involving “Or” When a single card is drawn from a standard 52-card deck, what is the probability that it will be a king or a diamond? Solution

  16. Example: Finding the Probability of an Event Involving “Or” If a single die is rolled, what is the probability of a 2 or odd? Solution These are mutually exclusive events.

  17. Example: Finding the Probability of an Event Involving “Or” • Of 20 elective courses, Emily plans to enroll in one, which she will choose by throwing a dart at the schedule of courses. If 8 of the courses are recreational, 9 are interesting, and 3 are both recreational and interesting, find the probability that the course she chooses will have at least one of these two attributes.

  18. Example: Finding the Probability of an Event Involving “Or” • Solution • If R denotes “recreational” and I denotes “interesting,” then • R and I are not mutually exclusive.

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