Section 11.1 Empirical and Theoretical Probabilities

Equally likely outcomes

If each outcome of an experiment has the same chance of occurring as any other outcome, we say that they are equally likely outcomes.

Theoretical Probability

Is determine through the study of POSSIBLE outcomes that can occur for an event

Empirical Probability

Is the relative frequency of an occurrence of an event and is determined by actual observations in an experiment. Empirical Probability is used when probabilities cannot be theoretically calculated.

Sum of Probability Example

See screenshot. Second example not seen is just another way the problem could have been worked in that if 4 cards were 8's then 48 cards were not so 48/52 also = 12/13

Event

A sub collection of the outcomes of an experiment

Experiment

A controlled operation that yeilds a set of results

The Law of Large Numbers

States that probability statement apply in practice to a large number of trials, not to a single trial. It is the relative frequency over the long run that is accurately predictable, not individual events or precise totals.

IMPORTANT PROBABILITY FACTS

1. The probability that an event can NOT occur is zero. 2. The probability that an event MUST occur is one. 3. Every probability is a number between zero and one; that is 0 is < or = P(E) < or = 1. 4. The Sum of the probabilities of all possible outcomes of an experiment is one.

Formula for Empirical Probability

P (E) = # if times an event has occurred / the total number of times the experiment has been performed

Formula for the Sum of Probabilities

P(A) + P(Not A) = 1. Or. P(Not A) = 1 - P(A)

Formula for Theoretical Outcomes

P(E) = Number of outcomes favorable to E / Total number of possible outcomes

Outcomes

The possible results of an experiment