1. Aim: What are the additional rules of probability? HW#4: complete worksheet titled: “applying probability” TEST TUESDAY 3/9/10

2. Two or more events Example1: at a large political gathering, one might wish to know, for a person selected at random, the probability that the person is a female or is a Republican. There are three possibilities: – The person is a female – The person is a Republican – The person is both a female and a Republican Example2: at the same gathering there are Republicans, Democrats, and Independents; if a person is selected at random, what is the probability that the person is a Democrat or an Independent? – There are two possibilities: The person is a Democrat The person is an Independent

3. Difference between two examples Mutually exclusive events: two events are mutually exclusive if they cannot occur at the same time (they have no outcomes in common) – One cannot be a Democrat and an Independent at the same time; must be one or the other

4. Addition Rule 1 When two events A and B are mutually exclusive, the probability of A or B will occur is – P(A or B) = P(A) + P(B) Example: a box contains 3 glazed doughnuts, 4 jelly doughnuts and 5 chocolate doughnuts. If a person selects a doughnut at random, find the probability that it is either a glazed doughnut or a chocolate doughnut P(glazed or chocolate) = P(glazed) + P(chocolate)

5. Summary Addition Rule 1

6. Addition Rule 2 When events are not mutually exclusive, then – P(A or B) = P(A) + P(B) – P(A and B) Example: In a hospital unit there are 8 nurses and 5 physicians; 7 nurses and 3 physicians are females. If a staff person is selected, find the probability that the subject is a nurse or a male. P(nurse or male) = P(nurse) + P(male) – P(male nurse)

7. Summary Addition Rule 2

8. For three events… The additive rules can be extended to three events: – Mutually Excusive Events: P(A or B or C) = P(A) + P(B) + P(C) – Non-Mutually Excusive Events P( A or B or C) = P(A) + P(B) + P(C) – P(A and B) – P(B and C) – P(A and C) + P(A and B and C)

9. Class Work 1.Determine which events are mutually exclusive and which are not, when a single die is rolled. A.Getting an odd number and getting an even number B.Getting a 3 and getting an odd C.Getting an odd number and getting a number less than 4 D.Getting a number greater than 4 and getting a number less than 4 2.At a political rally, there are 20 Republicans, 13 Democrats and 6 Independents. If a person is selected at random, find the probability that he or she is either a Democrat or an Independent. 3.On New Year’s Eve, the probability of a person diving while intoxicated is 0.32, the probability of a person having a driving accident is 0.09, and the probability of a person getting into an accident while intoxicated is 0.06. What is the probability of a person driving while intoxicated or having a driving accident? 4.A single card is drawn from a deck. Find the probability of selecting the following: A.A 4 or a diamond B.A club or a diamond C.A jack or a black card 5.If one card is drawn from an ordinary deck of cards, find the probability of getting the following A.A king or queen or a jack B.A club or a heart or a spade C.A king or a queen or a diamond D.An ace or a diamond or a heart