State Bayes Theorem and use it to calculate conditional probabilities

An extension of conditional probability is Bayes Theorem which can be written as: $$ P\left( A|B \right) =\frac { P\left( B|A \right) \ast P\left( A \right) }{ P\left( B \right) } $$ Example Given a population of students in which…

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Calculate probabilities using combinatorics, such as combinations and permutations

Permutations In probability, we may be interested in the possible arrangement of a set of objects. If we are interested in the order of the arrangement of the objects, we call this arrangement a permutation. Example: Consider flipping 2 coins….

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Define and calculate conditional probabilities

Given two events \(A\) and \(B\), the conditional probability of event \(A\) occurring, given that event \(B\) has occurred is the probability of event \(A\) and \(B\) occurring over the probability of event \(B\) occurring as shown in the formula…

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Define independence and calculate probability of independent events

Independent Events In probability, two events (\(A\) and \(B\)) are said to be independent if the fact that one event (\(A\)) occurred does not affect the probability that the other event (\(B\)) will occur Consider the experiment rolling a die…

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Calculate probabilities using the addition and multiplication rules

Addition Rule of Probability $$ P\left( A\cup B \right) =P\left( A \right) +P\left( B \right) -P\left( A\cap B \right) $$ The addition rule of probability states that the probability of event \(A\) or event \(B\) occurring is the probability of…

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Calculate probabilities of mutually exclusive events

\(A\) and \(B\) are mutually exclusive events if \(A\) and \(B\) cannot both occur at the same time. Example: When flipping a coin, the coin cannot land on head and tails at the same time so we consider the events…

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Define set functions, sample space, and events

In order to understand the concept of probability, it is useful to think about an experiment with a known set of possible outcomes. This set of all possible outcomes is called the sample space \((S)\). Sample space \((S)\) –set of…

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