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## M ARIO F . T RIOLA

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**STATISTICS**ELEMENTARY Section 3-3 Addition Rule MARIO F. TRIOLA EIGHTH EDITION**Compound Event**Any event combining 2 or more simple events Definition**Compound Event**Any event combining 2 or more simple events Notation P(A or B) = P (event A occurs or event B occurs or they both occur) Definition**General Rule**When finding the probability that event A occurs or event B occurs, find the total number of ways A can occur and the number of ways B can occur, but find the total in such a way that no outcome is counted more than once. Compound Event**Formal Addition Rule**P(A or B) = P(A) + P(B) - P(A and B) where P(A and B) denotes the probability that A and Bboth occur at the same time. Compound Event**Formal Addition Rule**P(A or B) = P(A) + P(B) - P(A and B) where P(A and B) denotes the probability that A and Bboth occur at the same time. Intuitive Addition Rule To find P(A or B), find the sum of the number of ways event A can occur and the number of ways event B can occur, adding in such a way that every outcome iscounted only once. P(A or B) is equal to that sum, divided by the total number of outcomes. Compound Event**Events A and B are mutually exclusive if they cannot occur**simultaneously. Definition**Events A and B are mutually exclusive if they cannot occur**simultaneously. Definition Total Area = 1 P(A) P(B) P(A and B) Overlapping Events Figures 3-5**Events A and B are mutually exclusive if they cannot occur**simultaneously. Definition Total Area = 1 Total Area = 1 P(A) P(B) P(A) P(B) P(A and B) Overlapping Events Non-overlapping Events Figures 3-5 and 3-6**Example: Mutually Exclusive**• Determine whether the events are mutually exclusive. • Selecting a student with a birthday in March • Selecting a student with a birthday in May**Example: Mutually Exclusive**• Determine whether the events are mutually exclusive. • Selecting a student with a birthday in March • Selecting a student with a birthday in May • The events ARE mutually exclusive.**Example: Mutually Exclusive**• Determine whether the events are mutually exclusive. • Selecting a student with a birthday in March • Selecting a student who was born on a Monday.**Example: Mutually Exclusive**• Determine whether the events are mutually exclusive. • Selecting a student with a birthday in March • Selecting a student who was born on a Monday. • The events are NOT mutually exclusive.**Example: Mutually Exclusive**• Determine whether the events are mutually exclusive. • Selecting a full-time UCLA student • Selecting a full-time University of Notre Dame student**Example: Mutually Exclusive**• Determine whether the events are mutually exclusive. • Selecting a full-time UCLA student • Selecting a full-time University of Notre Dame student • The events ARE mutually exclusive.**Example: Mutually Exclusive**• Determine whether the events are mutually exclusive. • Selecting a senior in high school. • Selecting a student with a part-time job.**Example: Mutually Exclusive**• Determine whether the events are mutually exclusive. • Selecting a senior in high school. • Selecting a student with a part-time job. • The events are NOT mutually exclusive.**Figure 3-7 Applying the Addition Rule**P(A or B) Addition Rule Are A and B mutually exclusive ? Yes P(A or B) = P(A) + P(B) No P(A or B) = P(A)+ P(B) - P(A and B)**Find the probability of randomly selecting a man or a boy.**Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 56 2223**Find the probability of randomly selecting a man or a boy.**Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 56 2223**Find the probability of randomly selecting a man or a boy.**P(man or boy) = 1692 + 64 = 1756 = 0.790 2223 2223 2223 Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 56 2223**Find the probability of randomly selecting a man or a boy.**P(man or boy) = 1692 + 64 = 1756 = 0.790 2223 2223 2223 Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 56 2223 * Mutually Exclusive ***Find the probability of randomly selecting a man or someone**who survived. Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 56 2223**Find the probability of randomly selecting a man or someone**who survived. Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 56 2223**Find the probability of randomly selecting a man or someone**who survived. P(man or survivor) = 1692 + 706 - 332 = 1756 2223 2223 2223 2223 Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 56 2223 = 0.929**Find the probability of randomly selecting a man or someone**who survived. P(man or survivor) = 1692 + 706 - 332 = 1756 2223 2223 2223 2223 Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 56 2223 = 0.929 * NOT Mutually Exclusive ***P(A) and P(A)**are mutually exclusive Complementary Events**P(A) and P(A)**are mutually exclusive All simple events are either in A or A. Complementary Events**P(A) and P(A)**are mutually exclusive All simple events are either in A or A. P(A) + P(A) = 1 Complementary Events**Rules of Complementary Events**P(A) + P(A) = 1**Rules of Complementary Events**P(A) + P(A) = 1 = 1 - P(A) P(A)**Rules of Complementary Events**P(A) + P(A) = 1 = 1 - P(A) P(A) = 1 - P(A) P(A)**Figure 3-8 Venn Diagram for the Complement of Event**A Total Area = 1 P (A) P (A) = 1 - P (A)**Example: Complementary Events**• If a person is randomly selected, find the probability that his or her birthday is not in October. Ignore the leap years.**Example: Complementary Events**• If a person is randomly selected, find the probability that his or her birthday is not in October. Ignore the leap years. • P(Birthday not in October)