wk 3: Simple probability and Binomial Distribution

These flashcards cover key terms and concepts related to Simple Probability and Binomial Distribution as discussed in the lecture.

Simple Probability

The foundation of probability theory which addresses the likelihood of events occurring based on known factors.

Event

The set of outcomes from an experiment in probability.

Probability Formula

The mathematical representation used to calculate likelihood, constrained between the values 0 and 1.

Complement (AC)

The opposite of an event A, representing all outcomes where A does not occur.

Independence

A condition where two events A and B do not influence each other's probabilities.

Mutually Exclusive Events

Events that cannot occur at the same time; the occurrence of one excludes the possibility of the other.

Binomial Distribution

A probability model used for discrete outcomes with only two possible results, such as success or failure.

Factorial (k!)

The product of all positive integers up to k, a key component in calculating probabilities in binomial distributions.

Success

The favorable outcome in a binomial distribution, representing the event of interest occurring.

Probability of Success (p)

The likelihood that a specific outcome will occur in the binomial distribution context.

n

The number of observations or trials in a binomial distribution experiment.

x (number of successes)

The count of successful outcomes observed in a set of trials or observations.

Probability of Exactly k Successes

The likelihood that there will be exactly k successful outcomes in n trials of a binary experiment.

Complement Rule

A rule stating that the probability of an event occurring is equal to one minus the probability of it not occurring.

At Least Two Successes

A condition in probability problems indicating the need to find the likelihood of two or more successful outcomes.

P(x=0)

The probability that the event has zero successes in a given number of trials in a binomial distribution.