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. Events Involving “Not” and “Or”
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. Operation or Connective (Symbol)
Correspondences
Set Theory
Logic
Arithmetic
Operation or Connective (Symbol)
Complement
Not
Subtraction
Union Or
Addition
Intersection
And
Multiplication

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.