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Probability & Statistics (Rules of Probability (Multiplication Rules…
Probability & Statistics
Probability is the likelihood of an event occurring, it is given by the ration of how many times an outcome occurs to all the possible outcomes.
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Language of Probability
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An outcome of a probability experiment is the result of a single trial of a probability experiment,
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Combinations: an r combination of elements of a set is an unordered selection of r elements from a set.
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Rules of Probability
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Rule 2: When an event cannot occur, the probability is zero.
Rule 3: When an event is certain to occur, the probability is 1.
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Rule 5: The probability that an event will not occur is equal to 1 minus the probability that the event will occur.
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Multiplication Rules
The multiplication rules can be used to find the probability of two or more events that occur in sequence.
Independent Events: Two events, A and B, are said to be independent if the fact that event A occurring does not affect the probability that event B occurs.
Dependent Events: the occurrence of the first event changes the probability of the occurrence of the second event.
Multiplication Rule 2: When two events A and B are dependent, the probability that the second event B occurs after the first event A has already occurred is written as:
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Conditional Probability
Allows us to modify or condition the probability when additional information about an event is know,
Applications: Diagnosis of medical conditions, Data analysis.
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