HARAMAYA UNIVERSITY COLLEGE OF HEALTH AND MEDICAL SCIENCES
DEPARTMENT OF PUBLIC HEALTH POST GRADUATE PROGRAM OF GPH and HSM
SUMMITED TO:- Mr. LEMAMA D.R (MPH)
SUMMITED BY:- GPH and HSM STUDNTS
Harar, Ethiopia
Wednesday, 15 December, 2021
Group Members and Students Name
1.
2.
3.
4.
5.
6.
1.
2.
3.
4.
5.
GPH
Zelalem Gizaw
Nathan Melese
Dawit Girma
Negash Asea
Mohamme Adus
Mohammd
HSM
Shemsudin Ahamd
Yusuf Ibrahim
Mahamed Muhamed
Ahmed Musa
Abduqadir
Presentation outline
• Introduction of Probability
• Properties of Probability
• Counting rules of Probability
• References
Introduction of Probability
• Chance of observing a particular outcome
• Likelihood of an event
• Assumes a “stochastic” or “random” process: i.e.. the outcome is
not predetermined - there is an element of chance
• An outcome is a specific result of a single trial of a probability
experiment.
Contin…
• Probability theory developed from the study of games of
chance like dice and cards.
• A process like flipping a coin, rolling a die or drawing a
card from a deck are probability experiments.
• Central to the understanding of inferential statistics
Some definitions in probability:• Experiment is any process with an uncertain outcome. An
experiment is a trial and all possible outcomes are events
• An Outcome (Sample point) is any result obtained in an
experiment.
• Event is something that may happen or not when the
experiment is performed (either occur or not)
• Events are represented by uppercase letters such as A, B, C,
etc
• A sample space is the set of all possible outcomes of a
probability experiment.
Some sample spaces for various probability experiments
Experiments
• Toss one coin
• Roll a die
• Answer a true/false question
• Toss two coins
Sample spaces
Head, tail
1, 2, 3, 4, 5, 6
True, false
Head-head, tail-tail, head-tail,tail-head
Contin…
Example When a "fair" coin is tossed, the possible results are either
head (H) or tail (T). Consider an experiment of tossing a fair coin twice.
A, What are the possible outcomes?
B, Give the sample space.
C, Give the event of at least one T appearing.
Answer
A, HH, HT, TH, TT
B, S = {HH, HT, TH, TT}
C, B = {HT, TH, TT}
Contin…
Probability can be defined as the number of times in which that event
occurs in a very large number of trials
Probability of an Event E
= a number between 0 and 1 representing the proportion of times that
event E is expected to happen when the experiment is done over and
over again under the same conditions
Properties of probability
1. The numerical value of a probability always lies between 0 and 1,
inclusive.
0 <= P(E) <=1
• A value 0 means the event can not occur
• A value 1 means the event definitely will occur
• A value of 0.5 means that the probability that the event will occur is
the same as the probability that it will not occur.
Contin…
2. The sum of the probabilities of all mutually exclusive
outcomes is equal to 1.
P(E1) + P(E2 ) + .... + P(En ) = 1.
3. For two mutually exclusive events A and B,
P(A or B ) = P(AUB)= P(A) + P(B).
If not mutually exclusive:
P(A or B) = P(A) + P(B) - P(A and B)
Contin…
4. The complement of an event A, denoted by Ā , is the
event that A does not occur
• Consists of all the outcomes in which event A does NOT
occur
P(Ā) = P(not A) = 1 – P(A)
• occurs only when A does not occur.
• These are complementary events.
Counting Rules (Basic Probability Rules)
1. Addition rule
• If events A and B are mutually exclusive: they cannot
appear at the same time
P(A or B) = P(A) + P(B)
P(A and B) = 0
• More generally:
P(A or B) = P(A) + P(B) - P(A and B)
P (event A or event B occurs or they both occur)
…addition
Examples
In tossing a coin, Head and Tail are mutually exclusive events
because. they cannot appear at the same time
Example
A question paper has two parts where one part contains 4
questions and the other 3 questions. If a student has to
choose only one question, from either part, in how many
ways can the student do it?
Solution: The student can choose one question in 4 + 3 = 7
ways
Multiplication principle
• If an event can occur in m different ways, and for every such
choice another event can occur in n different ways, then both
the events can occur in the given order in m × n different ways.
• That is, the number of ways in which a series of successive
things can occur is found by multiplying the number of ways
each thing can occur.
Multiplication
Example
Suppose Nuria wants to go from Harrar via Dire Dawa to Addis
Ababa. There are two minibuses from Harrar to Dire Dawa and 3
buses from Dire Dawa to Addis Ababa. How many ways are there for
Nuria to travel from Harrar to Addis Ababa?
Solution: Let M stand for Minibus and B stand for Bus.
There are (2 × 3) = 6 possible ways.
Reference
• Daniel Biostatistics book
• Mathematics Book
• Wakgari Deressa, PhD school of public health Addis Ababa
University ,Dec 2009 handout
Thank you!