we can't predict the individual outcomes, but we can hope to understand characteristics of their long run behavior
for any random phenomena, each trial generates an ______
we use the more general term ____ to refer to outcomes or combinations of outcomes
special event that is the collection of all possible outcomes
the probability of an event is its long run relative ________
independence means that the outcome of one trial is does or does not change the outcome of another?
______ stated that if the events are independent, then as the number of trials increases, the long-run relative frequency of an event gets closer and closer to its probability.
law of large numbers (LLN)
empirical probability is based on observing the event's outcome after many ______
why does the law of average not exist?
things balance out in the long run bc the unbalances events get outnumber by the large total number of outcomes, not by a string of opposite outcomes
theoretical probability can be computed by:
# of outcomes in "A" / total # of outcomes
if the probability of an event occurring is 0, the event can or can not occur
if the probability occurs, the event always or never occurs?
the probability of the set of all possible outcomes must be equal to what number?
one; P(S)=1 S represents the set of all possible outcomes and is called the sample space
the complement rule says that the probability of an event occurring is 1 - the probability that it does or does not occur
does not occur; P(A)= 1-P(A^c) A^c=complement
for two independent events, A and B, how do you find the probability that both A and B occur
multiply them together P(A and B)= P(A) x P(B)
if two events have no outcomes in common, they are
disjoint aka mutually exclusive
the addition rule allows us to add the probability of ______ events to get the probability that either event occurs
disjoint P(A or B) = P(A) + P(B)
the general addition rule calculates the probability of ______ of the two events occurs
either P(A or B)= P(A) + P(B)- P(A and B)
marginal probability depends only on totals found where on a table?
joint probabilities give the probability of how many events occurring together
probability that takes into account a given condition is called
disjoint events can or can not be independent
general multiplication rule calculates the probability that both of the two events occurs. TRUE or FALSE
beware of probabilities that don't add up to what number?
don't add probabilities of events if they are not _____
don't multiplu probability of events it they are not _________
probability is based on __________
long run relative frequencies
law of large numbers speaks only of long or short run behavior?
do not misinterpret the law of large numbers as the law of _____
tree diagrams can be constructed to help think through what type of problems?
probability for any event is between what 2 numbers?
0 and 1
probability of the sample space, S, the set of possible outcomes = what number?