Probability

Concepts

Sample space

Set of all possible outcomes of a random phenomenon - usually denoted by the letter .

Event

A subset of the sample space corresponding to a particular outcome or a group of possible outcomes.

Given two events :

• Union - contains all outcomes belonging to or both
• Intersection - contains of all outcomes common to both
• Complement - consists of all outcomes not in
• Mutually exclusive

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Probability

Probability

Proportion of times that an event occurs, in a long run of trials.

Axioms

• If are mutually exclusive, then .
• If is pairwise mutually exclusive then
• Additive Law of Probability

Independence

Two events are independent if:

Independence implies that two events do not influence each other.

Conditional Probability

The conditional probability of given is defined to be:

Law of Total Probability

If are mutually exclusive events within a sample space, where , are said to partition the sample space .

Then, for any event , we have:

Bayes Theorem

Given two events, on the sample space where , then

Suppose partition the sample space .

Epidemiological Terms

Sensitivity

The probability that the test is positive, given that the person has a disease.

Specificity

The probability that the test is negative, given that that the person does not have the disease.

Prevalence

The number of people who currently have the disease, divided by the number of people in population.

Confusion Matrix

Adapted from Wikipedia.

P + N	Predicted +ve	Predicted -ve
Actual +ve	TP	FN
Actual -ve	FP	TN