probability

The concept of probability is not a foreign to health workers. For example we may hear a physician say that a patient has 50-50 chance surviving from a certain operation, or physician may say that a patient has 95% a particular disease, so probability is a measure (or number) used to measure the chance of the occurrence of some event; this number is between 0 and 1. Probability may be classified into:
1- Classical probability
There are many conceptions in Classical probability such as:
Probability: is a measure (or number) used to measure the chance of the occurrence of some event. This number is between 0 and 1.
Sample Space: The set of all possible outcomes of an experiment is called the sample space (or Universal set) and is denoted by .
Mutually exclusive: is defined as the occurrence of one event exclude the occurrence of any others, or two event are said to be mutually exclusive if they can not occur simultaneously.
Equally likely: is the outcomes of an experiment are equally likely if the occurrences of the outcomes have the same chance.
Probability of an event: If the experiment has (n) equally likely outcomes, then the probability of the event (E) is:




Example: The rolling of an ordinary cubical die may result in any one of the six different faces facing upward. The six possible results are said mutually exclusive. The probability of getting any face is equal (1/6).
Example: If a card is drawn from ordinary deck, find the probability that is a heart. The number of possible outcome is 52, of which 13 hearts.
P (E) = 13/52 = 14
2- Relative frequency of probability
The relative frequency of an event (E).
Example: If we toss a coin 100 time and find it comes up head 60 times. We estimate the probability of head to be,
P (H) = 60/100 = 0.6
Some Operations on Events:
Set is defined as a collection of definite objects. The objects may be elements (ungrouped data) or values (grouped data).
1- Ungrouped data
Example: Let A and B be two events defined on:

A= {Patients 1, 2, 3, 4, 5, 6} =all assigned patients who are receiving drug therapy.
B= {Patients 2, 4, 7, 8, 9, 10, 11} =all assigned patients who are receiving psychotherapy.

Set operations:
1. The Union events ( ): consists of all elements belonging to either A or B or both A and B, if A occurs, or B occurs, or both A and B occur, from above example.
A B =all assigned patients who are receiving drug therapy,
psychotherapy, or both.
A B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

2. The Intersection events ( ): of two sets, A and B, is another set and consist of all outcomes elements that are in both A and B. if both A and B occur, from above example.
A B= Equal all assigned patients receiving both drug therapy
and psychotherapy.
A B= {2, 4}

3. The Complement events ( = not): consists of all outcomes of W but are not in A.




4. The Difference (A - B): The set consisting of all elements of (A) which do not belong to (B) is called the difference A and B.

A – B = {1, 3, 5, 6}