Probability

Gives the probability of an event for a finite sample space with equally likely outcomes.

States that probability lies between 0 for an impossible event and 1 for a sure event.

Relates the probability of an event not occurring to the probability that it occurs.

The sum of the probabilities of all mutually exclusive and exhaustive elementary events equals 1.

Gives the probability that at least one of two events occurs.

Gives the probability that at least one of three events occurs.

Expresses probabilities of joint complements using complements of unions and intersections.

Gives the probability that either event occurs, but not both simultaneously.

Gives the probability of event A given that event B has occurred, where P(B) > 0.

Computes the joint probability of two dependent events occurring together.

Criterion for two events A and B to be statistically independent.

Computes the total probability of event A partitioned across exhaustive and mutually exclusive events.

Finds the posterior probability of cause E_i given that event A has occurred.

Gives the expected value or mean of a discrete random variable.

Measures the dispersion of a discrete random variable about its mean.

Gives the probability of obtaining exactly r successes in n independent Bernoulli trials.

Gives the mean and variance of a binomial distribution with parameters n and p.