1. MATH 1107 Elementary Statistics Lecture 5 Addition Rules in Probability

2. Lets say that in order to maintain your HOPE scholarship, you must obtain either an A or a B in this class. Putting aside study time and unforeseen events, what is the probability of this occurring?

3. Since you cannot obtain both an A and a B, these are mutually exclusive events…or disjointed events So, the Prob (A or B) = P(A)+P(B) If your grade is random, then the answer is: Prob (A or B) = 1/5 + 1/5 = 2/5 or 40% Addition Rules in Probability

4. Now lets say that in order to retain your scholarship, you must pass either Statistics or English. What is the probability of this?

5. Since you can obtain passing grades in both, this is not considered a disjointed event. The probability for this outcome is: P(A or B) = P(A) + P(B) – P(A and B), where P(A and B) is the probability of passing both courses. This probability must be deleted to prevent double counting. Addition Rules in Probability

6. P(A) P(B) P(A and B)

7. MenWomenBoysGirlsTotal Survived3323182927706 Died136010435181517 Total169242264562223 What is the probability of selecting a man or a boy from the passenger list at random (regardless of their eventual fate)? Passengers on the Titanic Addition Rules in Probability

8. MenWomenBoysGirlsTotal Survived3323182927706 Died136010435181517 Total169242264562223 Passengers on the Titanic Addition Rules in Probability P(man or boy) = 1692 + 64 = 1756 or 79% 2223 2223 2223 This is an example of a disjointed events.

9. MenWomenBoysGirlsTotal Survived3323182927706 Died136010435181517 Total169242264562223 What is the probability of selecting a man or a survivor from the passenger list at random? Passengers on the Titanic Addition Rules in Probability

10. MenWomenBoysGirlsTotal Survived3323182927706 Died136010435181517 Total169242264562223 Passengers on the Titanic Addition Rules in Probability P(man or survivor) = 1692 + 706 - 332 = 2066 or 93% 2223 2223 2223 2223 This is an example of events that are not disjointed.

11. Addition Rules in Probability Positive TestNegative Test Pregnant805 Not Pregnant311 What is the probability of selecting a subject who is pregnant or tested positive? P(Preg or + Test) = 80 + 5 + 3 = 88 or 89% 99 99 99 99 P(Preg or + Test) = 83 + 85 - 80 = 88 or 89% 99 99 99 99

12. Addition Rules in Probability Positive TestNegative Test Pregnant805 Not Pregnant311 False Negative False Positive