T/F - Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run
True
When do we call a phenomenon random?
If individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions
What is the probability of any outcome of a random phenomenon?
The proportion of times the outcome would occur in a very long series of repetitions
Formula for probability
Number of times A occurs/Number of trials (n) = P(A)
What is the sample space of a random phenomenon?
The set of all possible outcomes
What is an event?
An outcome or a set of outcomes of a random phenomenon (the subset of a sample space)
What is a probability model?
A mathematical description of a random phenomenon consisting of two parts: a sample space (S) and a way of assigning probabilities to events
What is the value range for probability?
0 to 1
T/F - If you add up the probability of ALL events in a sample space, it MUST equal one
True
what is the probability that an event DOES NOT occur?
1 - the probability that the event will occur
If two events have NO outcomes in common, what is the probability that one or the other occurs?
The sum of their individual probabilities
What is the addition rule for disjoint events?
P(A U B) = P(A or B) = P(A) + P(B)
P(A does NOT occur) =
0
Name the general addition rule
P(A or B) = P(A)+P(B) - P(A and B)
P(A U B) = P(A)+P(B) - P(A intersection B)
What is conditional probability?
A means of adjusting probability in the light of new information
When P(B) > 0, the conditional probability of A given B (A|B) =
P(A|B) = P(A intersection B) / P(B) = P(A and B) / P(B)
Name the general multiplication rule
P(A and B) = P(A intersection B) = P(A|B)P(B) = P(B|A)P(A)
When do you use the multiplication rule?
If the question states the probability of A given B, use P(A|B)P(B)
If the question states the probability of B given A, use P(B|A)P(A)
Two events A and B that both have positive probability are independent IF
P(B|A) = P(B) and P(A|B) = P(A)
What is the multiplication rule for independent events?
P(A intersection B) = P(A) X P(B)
We use Venn Diagrams to solve problems involving...
Unions and intersections of two or more events
We use tree diagrams to solve problems involving...
Conditional probability
Bayes Theorem provides a method for finding...
P(A|B) from P(B|A)