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Introduction to Probability - Coggle Diagram
Introduction to Probability
Important Probabilities in Heath Care
Prevalence: the total number of cases in the population, divided by the number of individuals in the population.
Incidence: the probability that a person with no prior disease will develop disease over some specified time period
Sensitivity of a diagnostic or screening test: the probability the person tests positive, given the person has the disease.
Specificity of a diagnostic or screening test: the probability the person tests negative, given the person does not have the disease.
Survival probability: the probability an individual survives beyond a certain time
Scenarios for Probability
The Relative Frequency Interpretation: applies to situations that can be repeated over and over again (coin flip)
The Subjective/Personal-Probability: the degree to which a given individual believes the event will happen. (Bayesian
Terminology with probability and more than one probability variable
The event that A does not occur is called the complement of A and s denoted π΄π. ( 1- P(A))
The event that both A and B occur is called the intersection and is denoted π΄ β© π΅ (smaller probability)
The event that either A or B occurs is called the union and is
denoted π΄ βͺ π΅ (larger probability)
Intersection
The event that both A and B occur is called the intersection and is denoted π΄ β© π΅ (smaller probability)
If A and B are independent, and only if they are independent, then the probability of A or B occurring is the product of the two individual probabilities; π (π΄ β© π΅) = π (π΄) β π (π΅)
Union
The event that either A or B occurs is called the union and is
denoted π΄ βͺ π΅ (larger probability)
π (π΄ βͺ π΅) = π (π΄) + π (π΅)βπ (π΄ β© π΅) (these intersect and cannot be counted twice. need to minus) These are not mutually exclusive events and can both happen.
π (π΄ βͺ π΅) = π (π΄) + π (π΅) for disjointed/mutually exclusive events
Mutually Exclusive and Independent Variables
Two events are mutually exclusive if they cannot occur at the same time; in other words, the occurrence of one event excludes the occurrence of the other.
Mutually Exclusive: P(A β© B) = 0
Two events are independent if the occurrence of one event does not affect the occurrence of the other.
Independent: P(A β© B) = P(A). P(B)