Probability

The collection of all possible outcome values. The same space has a probability of 1.

Two events are disjoing or mutually exclusive if they have no outcomes in common.

If A and B are disjoint, then the probability of A or B is P(a)+ P(B)

For any two events, A and B, the probability of A or B is P(A)+P(B)-P(A and B)

P(A and B)/ P(B)

Two events are independent if knowing whether one event occurs does not alter the probability that the other event occurs

If A and B are independent events, then the probability of A and B is P(A and B)= P(A) x P(B)

For any two events, A and B, the probability of A and B is P(A and B)= P(A) x P(AlB)

A display of conditional events or probabilities that is helpful in thinking through conditioning

A phenomenon is random if we know what outcomes could happen, but not which particular values will happen

The probability of an event is a number between 0 and 1 that reports the liklihood of the event's occurrence. A probability can be derived from equally likely outcomes, from the long-run relative frequency of the event's occurrence, or from known probabilities. We wrie P(A) for the probability of the event A.

A single attempt or realization of a random phenomenon

The outcome of a trial is the value measured, observed, or reported for an individual instance of that trial

A collection of outcomes. Usually we identify events so that we can attach probabilities to them. We denote events with bold capital letters such as A, B , or C

States that the long-run relative frequency of repeated independent events settles down to the true relative frequency as the number of trials increases