Chapter 5 - QMB2100

Question 1

What is a probability?

Answer 1

A value between 0 and 1, inclusive, describing the relative possibility (chance or likelihood) an event will occur.

Question 2

What are the 3 ways probabilities are communicated?

Answer 2

Decimal, percent, or fraction.

Question 3

What does the scale from 0 to 1 indicate?

Answer 3

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.

Question 4

What is the term odds?

Answer 4

The likelihood of an event.

Question 5

What is experiment?

Answer 5

A process that leads to the occurrence of one and only one of several possibilities.

Question 6

What is outcome?

Answer 6

A particular result of an experiment.

Question 7

What is event?

Answer 7

A collection of one or more outcomes of an experiment.

Question 8

What are the 3 ways to assign a probability to an event?

Answer 8

Classical, empirical, and subjective.

Question 9

What is classical probability?

Answer 9

Probability that assumes that the outcomes of an experiment are equally likely.

Question 10

How is the classical probability computed?

Answer 10

Probability of an event = number of favorable outcomes / number of all possible outcomes

Question 11

What are the three formulas used to help determine the number of all possible outcomes?

Answer 11

Multiplication formula, permutation formula, and combination formula.

Question 12

What is the multiplication formula?

Answer 12

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.

Question 13

What is permutation?

Answer 13

Any arrangement of r objects selected from a single group of n possible objects.

Question 14

What is the permutation formula?

Answer 14

nPr = n! / (n-r)!; where nPr is the permutations, n is the total number of objects and r is the number of objects selected.

Question 15

What is a combination?

Answer 15

An event of outcomes when the order of the outcomes does not matter.

Question 16

What is the combination formula?

Answer 16

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.

Question 17

What is an empirical probability?

Answer 17

The probability of an event based on a collection of observed data.

Question 18

How is the empirical probability calculated?

Answer 18

Empirical probability = number of times the event occurs / total number of observations.

Question 19

What is the law of large numbers?

Answer 19

Over a large number of trials, the empirical probability will approach its true probability.

Question 20

What is subjective probability?

Answer 20

The likelihood of a particular event happening that is assigned by an individual based on whatever information is available.

Question 21

What are the 2 rules of addition for computing probabilities?

Answer 21

The special rule of addition and the general rule of addition.

Question 22

What is one condition for the special rule of addition?

Answer 22

The events must be mutually exclusive.

Question 23

What is mutually exclusive?

Answer 23

The occurrence of one event means that none of the other events can occur at the same time.

Question 24

What does the special rule of addition states?

Answer 24

The probability of one or the other event’s occurring equals the sum of their probabilities.

Question 25

What is the formula for the special rule of addition?

Answer 25

P(A or B) = P(A) + P(B)

Question 26

What is collectively exhaustive?

Answer 26

When the list of outcomes is complete; at least one of the events must occur when an experiment is conducted.

Question 27

What happens when a list of outcomes is mutually exclusive and collectively exhaustive?

Answer 27

The sum of the probabilities is equals to 1.

Question 28

What is the complement rule?

Answer 28

Is a rule used to determine the probability of an event occurring by subtracting the probability of the event not occurring from 1.

Question 29

What is the formula for the complement rule?

Answer 29

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.

Question 30

What is the general rule of addition?

Answer 30

Is the rule of addition used when the probability of two events are not mutually exclusive.

Question 31

What is joint probability?

Answer 31

A probability that measures the likelihood of two or more events will happen cocurrently.

Question 32

What is the formula for the general rule of addition?

Answer 32

P(A or B or both) = P(A) + P(B) - P(A and B)

Question 33

What are the 2 rules of multiplication?

Answer 33

The special rule of multiplication and the general rule of multiplication.

Question 34

What does the special rule of multiplication requires?

Answer 34

That the two events A and B are independent.

Question 35

What does independence means?

Answer 35

The occurrence of one event has no effect on the probability of the occurrence of another event.

Question 36

What is the formula for the special rule of multiplication?

Answer 36

P(A and B) = P(A)P(B)

Question 37

When is the general rule of multiplication used?

Answer 37

When two events are dependent. The probability of the second event depends on the first event. The second event is a conditional probability.

Question 38

What is a conditional probability?

Answer 38

The probability of a particular event occurring, given that another event has occurred.

Question 39

What is the formula for the general rule of multplication?

Answer 39

P(A and B) = P(A)P(B l A); where P(B l A) represents the conditional probability.

Question 40

What is a contingency table?

Answer 40

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.

Question 41

What is a tree diagram?

Answer 41

Is another form of visually organizing and calculating probabilities where he branches of a tree diagram are labeled with probabilities.

Question 42

What is the formula for Bayes' Theorem?

Answer 42

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.

Question 43

What is a prior probability?

Answer 43

The initial probability based on the present level of information.

Question 44

What is a posterior probability?

Answer 44

A revised probability based on additional information.

Question 45

What is the formula to find a permutation in excel?

Answer 45

=PERMUT(number, number_chosen); where number is n and number_chosen is r.

Question 46

What is the formula to find the combination in excel?

Answer 46

=COMBIN(number, number_chosen)