7.1 The Multiplication Rule for Counting

7.2 Permutations

Permutations are used to count subsets when order matters; combinations work when order doesn't matter.
Combinations can also be computed using factorials.

We identify the sample space of an experiment by identifying all of its possible outcomes.
Tables can help us find a sample space by keeping the possible outcomes organized.
Tree diagrams provide a visualization of the sample space of an experiment that involves multiple stages.

The theoretical probability of an event is the ratio of the number of equally likely outcomes in the event to the number of equally likely outcomes in the sample space.
Empirical probabilities are computed by repeating the experiment many times, and then dividing the number of replications that result in the event of interest by the total number of replications.
Subjective probabilities are assigned based on subjective criteria, usually because the experiment can’t be repeated and the outcomes in the sample space are not equally likely.
The probability of the complement of an event is found by subtracting the probability of the event from one.

We use permutations and combinations to count the number of equally likely outcomes in an event and in a sample space, which allows us to compute theoretical probabilities.

Odds are computed as the ratio of the probability of an event to the probability of its compliment.

The Addition Rule is used to find the probability that one event or another will occur when those events are mutually exclusive.
The Inclusion/Exclusion Principle is used to find probabilities when events are not mutually exclusive.

Conditional probabilities are computed under the assumption that the condition has already occurred.
The Multiplication Rule for Probability is used to find the probability that two events occur in sequence.

Binomial experiments result when we count the number of successful outcomes in a fixed number of repeated, independent trials with a constant probability of success.
The binomial distribution is used to find probabilities associated with binomial experiments.
Probability density functions (PDFs) describe the probabilities of individual outcomes in an experiment; cumulative distribution functions (CDFs) give the probabilities of ranges of outcomes.

The expected value of an experiment is the sum of the products of the numerical outcomes of an experiment with their corresponding probabilities.
The expected value of an experiment is the most likely value of the average of a large number of replications of the experiment.