This document provides an introduction and overview of probability concepts for a biostatistics course. It includes the instructor's background and qualifications, defines probability, provides examples of calculating probability for different scenarios, and describes the key concepts of frequentist and Bayesian probability, mutually exclusive and independent events, and the additive and multiplicative rules of probability. Examples are provided to demonstrate how to calculate probabilities for multiple events.

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

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 (%)
Positive 59 (29.5)
Negative 151 (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:
Group n %
0 45 45
A 29 29
B 21 21
AB 5 5
Total 100 100
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.