1. Biostatistics course Part 4 Probability Dr. C. Nicolas Padilla Raygoza Department of Nursing and Obstetrics Division of Health Sciences and Engioneering Campus Celaya Salvatierra University of Guanajuato

2. Biosketch Medical Doctor by University Autonomous of Guadalajara. Pediatrician by the Mexican Council of Certification on Pediatrics. Postgraduate Diploma on Epidemiology, London School of Hygine and Tropical Medicine, University of London. Master Sciences with aim in Epidemiology, Atlantic International University. Doctorate Sciences with aim in Epidemiology, Atlantic International University. Professor Titular A, Full Time, University of Guanajuato. Level 1 National Researcher System padillawarm@gmail.com raygosan@ugto.mx padillawarm@gmail.comraygosan@ugto.mx

3. Competencies The reader will define what is probability. He (she) will know and describe additive law. He (she) will know and describe multiplicative law.

4. Definitions Probability is the possibility that an event occur. If we repeat many times an experiment, when obtained expected result, it is divided between number of experiments to know the probability. If a result is sure that occur the probability will be 1 (100%). If a event is sure that does not occur the probability will be 0.

5. Examples If we throw a coin in the air once, the probability to obtain face is ½, because only we can obtain face or cross. If we throw a dice once, the probability to obtain a 4 is 4/16, because there are 6 sides in the dice. If we have a box with 100 balls: 5 blue, 5 green, 10 orange, 10 yellow, 20 red, 20 white and 30 brown, the higher probability is to obtain a brown ball, 30/100 = 0.3 = 30%.

6. Probability Frequentist (objective): Probability that an event will occur, is the probability of times that the result will be observe if we repeat the experiment many times. Bayesian (subjective): It permit the explicit use of external judgment and believes in the analysis and interpretation of data.

7. Probability An experiment is a process planed to obtain data. An opposite event of the interest is called complementary event and its probability is obtained subtracting of 1 the probability of interest event. Probability to have amebiasis is 59/200= 0.295= 29.5% Probability of does not have amebiasis es 151/200= 0.705 = 70.5% or 1 - 0.0.295=0.705 = 70.5% Results for E. histolytic n (%) Positive59 (29.5) Negative151 (70.5)

8. Probability If I throw a dice, the probability to obtain 6 is 1/6; if throw the dice 20 times will be difficult to obtain a 6 in three of 20 times that I throw the dice; but if I throw it 1000 times, obtained a 6 is more near at 16.7%. Proportion that vary up or down of 16.7% is a consequence of chance.

9. Probability rules Mutually excluded events Two events are mutually excluded if the occurrence of an event avoid the occurrence of the other. For example If a baby is male, cannot be female. If a child had positivity for E. histolytic, can not had negativity. The probability of occurrence of two mutually excluded events, is the probability of occurrence of an event or another, and we can obtain the probability, add the individual probabilities of each event.

10. Probability rules Example 100 new born in a maternity of Celaya 55 were females and 45 males Probability to be female 55/100 = 0.55 Probability to be male 45/100=0.45 Probability to be anyone = 0.55 + 0.45 = 1.00

11. Probability rules Example 200 children with a test for E. histolytic 59 had positive result. 151 had negative result Probability of positivity for E. histolytic was 59/200= 0.295 Probability of negativity for E. histolytic was 51/200 = 0.705 Probability for positive or negative result was 0.295 + 0.705 = 1.00

12. Probability rules Independent events Two events are independents if the occurrence of a event does not affect the occurrence of the second event. Example If the first new born is male, does not affect that the next be female. Probability of two independent events is obtained multiplying individual probabilities of each event. This is the multiplicative law of probability.

13. Probability rules Example In a blood bank, they determined blood groups: Groupn% 045 A29 B21 AB55 Total100 What is the probability of next two persons will be 0 group? Is it mutually excluded or independent?

14. Probability rules If the next person has 0 group does not interfere with that the second next person has 0 group, because of this are independent events. Their individual probabilities, are multiplied: 0.45 x 0.45 = 0.2025 = 20.25%

15. Probability rules Example 100 new born in a maternity in Celaya 55 were females and 45 males Probability of to be women was 55/100 =0.55 Probability to be boy was 45/100 = 0.45 What is the probability of the next three deliveries are females?

16. Probability rules Example They are excluded mutually events, and their individual probabilities are multiplied. 0.55 x 0.55 x 0.55 = 0.1664 = 16.64%

17. Bibliografía 1.- Last JM. A Dictionary of epidemiology. New York, 4ª ed. Oxford University Press, 2001:173. 2.- Kirkwood BR. Essentials of medical stastistics. Oxford, Blackwell Science, 1988: 1-4. 3.- Altman DG. Practical statistics for medical research. Boca Ratón, Chapman & Hall/ CRC; 1991: 1-9.