Statistics 4.1 Introduction to Probability

Empirical (or Experimental) Probability Formula

In experimental probability, if E is an event, then P(E), read "the probability that E occurs," is given by P(E)=f/n where f is the frequency of event E and n is the total number of times the experiment is performed.

Probability Experiment

Or Trial, is any process in which the result is random in nature. Ex: flipping a coin, tossing a pair of dice, or drawing a raffle ticket.

Sample Space

The set of all possible outcomes for a given probability experiment.

Rounding Rule

When calculating probability, either give the exact fraction or a decimal rounded to four decimal places. If the probability is extremely small, it is permissible to round the decimal to the first nonzero digit.

Tree Diagram

allows the outcomes to be organized in a systematic manner.

Classical Probability Formula

if all outcomes are equally likely to occur, then P(E), read "the probability that E occurs," is given by P(E)= n(E)/n(S) where n(E) is the number of outcomes in the event and n(S) is the number of outcomes in the sample space.

Outcome

individual result from a probability experiment

Event

is a subset of outcomes of the sample space. Note that it is possible for an event to include the entire sample space.

Empirical (or Experimental) probability

is found by performing an experiment. The empirical (or experimental) probability of an event is calculated by dividing the number of times an event occurs by the total number of trials performed.

Subjective Probability

is simply an educated guess regarding the chance that an event will occur. The accuracy of the probability depends on the expertise of the person giving the probability.

Classical Probability (also called theoretical probability)

is the most precise type of probability. it is calculated by taking all possible outcomes for an experiment into account. Classical probability states that if all outcomes are equally likely, the probability of an event is equal to the number of outcomes included in the event divided by the total number of outcomes in the sample space. Remember the outcomes must be equally likely.

Law of Large Numbers

says that the greater the number of trials, the closer the experimental probability will be to the true probability.