Probability theory is the mathematical framework for analyzing the likelihood of events, ranging from simple to complex scenarios. It includes concepts such as independent and dependent events, mutually exclusive events, and compound events. Understanding these principles is crucial for calculating probabilities using addition and multiplication rules, and visual aids like tree diagrams can be instrumental in this process.
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Probability is a branch of mathematics that deals with calculating the likelihood of occurrence of different events
Definition of an event
An event is a set of outcomes of an experiment, or a single outcome, to which a probability is assigned
Definition of sample space
The set of all possible outcomes of an experiment is called the sample space
The probability of an event is a number between 0 and 1, inclusive, with 0 representing impossibility and 1 representing certainty
Probabilities can be expressed as fractions, decimals, or percentages
To calculate the probability of an event, one divides the number of favorable outcomes by the total number of possible outcomes in the sample space
Independent Events
Events that do not affect each other's probabilities
Dependent Events
Events that influence each other's probabilities
Mutually Exclusive Events
Events that cannot occur at the same time
Events that involve the combination of two or more individual events
The probability of mutually exclusive events occurring is found by adding their individual probabilities
The probability of independent events occurring together is found by multiplying their individual probabilities
Visual representations used to calculate the total probability of compound events by adding the probabilities of all possible paths
Probability theory is used to determine the likelihood of simple events
Probability theory is also used to analyze and calculate the probabilities of more complex events involving multiple outcomes
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Define probability in mathematics.
Probability measures likelihood of event occurrences, ranging from 0 (impossible) to 1 (certain).
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What is an event in probability?
An event is a single outcome or a set of outcomes from an experiment to which a probability is assigned.
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What constitutes a sample space?
Sample space is the set of all possible outcomes of a probabilistic experiment.
