Probability Rules
- Probability- the chance of an event occurring
- Random experiment- an experiment in which the outcome is uncertain
- Probability is a number between 0 and 1
- Impossible event- has a probability of 0 (guaranteed not to happen)
- Certain event- has a probability of 1 (guaranteed to happen)
- Sum of probabilities for all possible outcomes=1
- Subjective probability- based on personal opinion
- Theoretical probability- based on formulas
- Experimental probability- based on the results of a random experiment
- Law of large numbers- if we repeat an experiment a large number of times, the results that we see experimentally should be closer to what we would expect to see theoretically
- Sample space- collection of all possible outcomes for an experiment
- Observation- the observed outcome of a random experiment
- Event- a subset of the sample space, a collection of outcomes
- Complement- the subset of all outcomes within the sample space that are not in the event A of interest
- Intersection (A and B)- the event containing all of the elements that are common to both A and B
- Union (A or B)- the event containing all of the elements that belong to either A only, B only, or both A and B
- Mutually exclusive- events that have no outcomes in common
- Correct positive- test results indicates that the condition is present, and it is
- False positive- test results indicates that the condition is present, but it is not
- False negative- test results indicates that the condition is not present, but it is
- Correct negative- test results indicates that the condition is not present, and it is not
- Sensitivity- the probability that the test will give a positive result, given that the condition tested for is present
- P (positive result | condition is present)
- Specificity- the probability that the test will give a negative result, given that the condition tested for is not present
- P (negative result | condition is not present)
- Ideally we want both the sensitivity and specificity of a test to be high