##### 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…

##### 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….

##### 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…

##### 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…

##### 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…

##### 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…

##### 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…