Chapter 5 - QMB2100 Flashcards
What is a probability?
A value between 0 and 1, inclusive, describing the relative possibility (chance or likelihood) an event will occur.
What are the 3 ways probabilities are communicated?
Decimal, percent, or fraction.
What does the scale from 0 to 1 indicate?
Probabilities close to 0 indicate that the chance of an event happening are very unlikely and close to 1 indicates hat the chance of an event happening are very likely.
What is the term odds?
The likelihood of an event.
What is experiment?
A process that leads to the occurrence of one and only one of several possibilities.
What is outcome?
A particular result of an experiment.
What is event?
A collection of one or more outcomes of an experiment.
What are the 3 ways to assign a probability to an event?
Classical, empirical, and subjective.
What is classical probability?
Probability that assumes that the outcomes of an experiment are equally likely.
How is the classical probability computed?
Probability of an event = number of favorable outcomes / number of all possible outcomes
What are the three formulas used to help determine the number of all possible outcomes?
Multiplication formula, permutation formula, and combination formula.
What is the multiplication formula?
Total number of arrangements = (m)(n); where m is the number of possibilities for an event and n is the number of possibilities for another event.
What is permutation?
Any arrangement of r objects selected from a single group of n possible objects.
What is the permutation formula?
nPr = n! / (n-r)!; where nPr is the permutations, n is the total number of objects and r is the number of objects selected.
What is a combination?
An event of outcomes when the order of the outcomes does not matter.
What is the combination formula?
nCr = n! / r!(n-r)!; where nCr is the number of combinations, n the total number of objects, and r the number of objects selected.
What is an empirical probability?
The probability of an event based on a collection of observed data.
How is the empirical probability calculated?
Empirical probability = number of times the event occurs / total number of observations.
What is the law of large numbers?
Over a large number of trials, the empirical probability will approach its true probability.
What is subjective probability?
The likelihood of a particular event happening that is assigned by an individual based on whatever information is available.
What are the 2 rules of addition for computing probabilities?
The special rule of addition and the general rule of addition.
What is one condition for the special rule of addition?
The events must be mutually exclusive.
What is mutually exclusive?
The occurrence of one event means that none of the other events can occur at the same time.
What does the special rule of addition states?
The probability of one or the other event’s occurring equals the sum of their probabilities.
What is the formula for the special rule of addition?
P(A or B) = P(A) + P(B)
What is collectively exhaustive?
When the list of outcomes is complete; at least one of the events must occur when an experiment is conducted.
What happens when a list of outcomes is mutually exclusive and collectively exhaustive?
The sum of the probabilities is equals to 1.
What is the complement rule?
Is a rule used to determine the probability of an event occurring by subtracting the probability of the event not occurring from 1.
What is the formula for the complement rule?
P(A) = 1 - P(~A); where P(~A) is the probability of an event not occurring and P(A) is the probability of an event occurring.
What is the general rule of addition?
Is the rule of addition used when the probability of two events are not mutually exclusive.
What is joint probability?
A probability that measures the likelihood of two or more events will happen cocurrently.
What is the formula for the general rule of addition?
P(A or B or both) = P(A) + P(B) - P(A and B)
What are the 2 rules of multiplication?
The special rule of multiplication and the general rule of multiplication.
What does the special rule of multiplication requires?
That the two events A and B are independent.
What does independence means?
The occurrence of one event has no effect on the probability of the occurrence of another event.
What is the formula for the special rule of multiplication?
P(A and B) = P(A)P(B)
When is the general rule of multiplication used?
When two events are dependent. The probability of the second event depends on the first event. The second event is a conditional probability.
What is a conditional probability?
The probability of a particular event occurring, given that another event has occurred.
What is the formula for the general rule of multplication?
P(A and B) = P(A)P(B l A); where P(B l A) represents the conditional probability.
What is a contingency table?
A table used to classify sample observations according to tow or more identifiable categories or classes; is a cross tabulation that simultaneously summarizes two variables of interest and their relationship.
What is a tree diagram?
Is another form of visually organizing and calculating probabilities where he branches of a tree diagram are labeled with probabilities.
What is the formula for Bayes’ Theorem?
P(Ai l B) = P(Ai)P(B l Ai) / [P(A1)P(B l A1) + P(A2)P(B l A2)]; where Ai refers to either event, A1 is an event and A2 is another event, P(A1) and P(A2) are prior probabilities and P(B l A1) and P(B l A2) are posterior probabilities.
What is a prior probability?
The initial probability based on the present level of information.
What is a posterior probability?
A revised probability based on additional information.
What is the formula to find a permutation in excel?
=PERMUT(number, number_chosen); where number is n and number_chosen is r.
What is the formula to find the combination in excel?
=COMBIN(number, number_chosen)
