Definition: A binomial distribution B(n,p) describes the number of successes in n independent trials, each with probability p of success.

Highlight: For a random variable X following a binomial distribution, E(X) = np represents the expected value, and V(X) = np$1-p$ represents the variance.

Example: Calculator functions for binomial probability calculations include binom Fdp(n,p,k) for individual probabilities and binom FRep(n,p,k) for cumulative probabilities.

Vocabulary: Bernoulli trials are independent repeated experiments with exactly two possible outcomes (success or failure) and constant probability across trials.

Definition: Conditional probability is expressed as PA(B), representing the probability of event B occurring given that event A has occurred.

Example: A probability tree diagram shows branching paths with probabilities, where each branch represents a possible outcome and contains the associated probability value.

Highlight: The total probability formula states that P(B) = P(A∩B) + P(Ā∩B), combining all possible ways an event can occur.

Vocabulary: Independent events are those where the occurrence of one event does not affect the probability of the other event occurring.