Stats Ch 5 terms
Event
An event is any collection of outcomes from a probability experiment. An event consists of one outcome or more than one outcome. We will denote events with one outcome, sometimes called simple events, e i . In general, events are denoted using capital letters such as E.
unusual event
An unusual event is an event that has a low probability of occurring.
The Law of Large Numbers
As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome.
Compute and Interpret Probabilities Using the Empirical Method
Because probabilities deal with the long-term proportion a particular outcome is observed, we begin our discussion of determining probabilities using the idea of relative frequency. Probabilities computed in this manner rely on empirical evidence, that is, evidence based on the outcomes of a probability experiment.
An experiment has equally likely outcomes when each outcome has the same probability of occurring.
For example, in throwing a fair die once, each of the six outcomes in the sample space, { 1 , 2 , 3 , 4 , 5 , 6 } , has an equal chance of occurring. Contrast this situation with a loaded die in which a five or six is twice as likely to occur as a one, two, three, or four.
Addition Rule for Disjoint Events
If E and F are disjoint (or mutually exclusive) events, then P ( E or F ) = P ( E ) + P ( F )
Complement Rule
If E represents any event and E c represents the complement of E, then P ( E c ) = 1 − P ( E )
Computing Probability Using the Classical Method
If an experiment has n equally likely outcomes and if the number of ways that an event E can occur is m, then the probability of E, P(E), is P ( E ) = number of ways that E can occur number of possible outcomes = m n (2) So, if S is the sample space of this experiment, P ( E ) = N ( E ) N ( S ) (3) where N(E) is the number of outcomes in E, and N(S) is the number of outcomes in the sample space.
Complement of an Event
Let S denote the sample space of a probability experiment and let E denote an event. The complement of E , denoted E c , is all outcomes in the sample space S that are not outcomes in the event E.
Probabilities Using the Empirical Approach
The probability of an event E is approximately the number of times event E is observed divided by the number of repetitions of the experiment. P ( E ) ≈ relative frequency of E = frequency of E number of trials of experiment (1)
independent events
Two events E and F are independent if the occurrence of event E in a probability experiment does not affect the probability of event F. Two events are dependent if the occurrence of event E in a probability experiment affects the probability of event F.
If an event is impossible, the probability of the event is
Zero
