Chapter 4

Question 1

An experiment

Answer 1

A process that, when performed, results in one and only one of many observations.

Question 2

Outcomes

Answer 2

The observations from the experiment.

Question 3

Sample space

Answer 3

The collection of all outcomes for an experiment is called a sample space.
Ex: tree diagrams

Question 4

Event

Answer 4

A collection of one or more of the outcomes of an experiment.

Question 5

2 types of events

Answer 5

1. Compound event
2. Simple event

Question 6

Simple event

Answer 6

A event that includes one and only one of the final outcomes for an experiment.
Denoted by Ei
Ex: tossing 2 heads or a heads tails

Question 7

Compound event

Answer 7

A collection of more than one outcome for an experiment.
Ex: tossing at least one head

Question 8

Probability

Answer 8

The numerical measure of the likelihood that a specific event will occur.

Question 9

2 properties of probability

Answer 9

1. The probability of an event will always lie between 0 and 1
2. The sum of probabilities of all simple events (or final outcomes) for an experiment is always 1

Question 10

Classical probability

Answer 10

If the probability in an experiment is equally likely.

Question 11

Classical probability for a simple event

Answer 11

P = 1/ total number of outcomes

Question 12

Classical probability for a compound event

Answer 12

P = number of outcomes favourable to a / total number of outcomes for the experiment

Question 13

Relative frequency

Answer 13

If the outcomes of experiments are not equally likely.
Gives an approximate probability
P = frequency of event A/ sample size

Question 14

Law of large numbers

Answer 14

If an experiment is repeated again and again, the probability of an event obtained from the relative frequency approaches the actual (or theoretical) probability.

Question 15

Subjective probability

Answer 15

The probability assigned to an event based on subjective judgement, experience, information, and belief.
A guess.

Question 16

Marginal probability

Answer 16

The probability of a single event without consideration of any other event.

Question 17

Conditional probability

Answer 17

The probability that an event will occur given that another has already occurred.
Probability of A given B = P(A| B)

Question 18

Mutually exclusive events

Answer 18

Events that cannot occur together.
Ex: toss a coin

Question 19

Independent events

Answer 19

2 events where one does not affect the probability or the occurrence of the other.
P (a|b) = P(A) or P (b|a) = P(B)

Question 20

Dependent events

Answer 20

If the events occur where one event affects the probability of the occurrence of the other events.
P(a|b) does not = P(A) or P (b|a) does not = P(B)

Question 21

Complementary events

Answer 21

Complement of A = Ac or A bar
Ac = the event that includes all the outcomes for an experiment that are not in A.
Opposite of the event A.

Question 22

Intersection of events

Answer 22

The intersection of events A and B represents the collection of all outcomes that are common to both A and B.
A and B = A n B

Question 23

Joint probability

Answer 23

The probability of the intersection of two events.

Question 24

Joint probability of independent events

Answer 24

P(A n B) = P(A) x P(B)
Can be extended to more than two independent events.

Question 25

Joint probability of dependent events

Answer 25

P(A n B) = P(A) x P(B | A) P(A n B) = P(B) x P(A | B)

Question 26

Joint probability of mutually exclusive events

Answer 26

It is always zero. They can never happen at the same time.

Question 27

Union of events

Answer 27

The union of events A and B represents the collection of all outcomes that belong to either A or B or to both A and B. A u B = A or B

Question 28

Probability of 2 mutually nonexclusive events.

Answer 28

P(A | B) = P(A) + P(B) - P(A and B)

Question 29

Probability of 2 mutually non-exclusive events.

Answer 29

P(A n B) = P(A) + P(B)

Question 30

Calculating total outcomes

Answer 30

The total number of outcomes for an event comes from multiplying the number of outcomes from each individual experiment.

Question 31

Factorials

Answer 31

n! = n factorial Represents the products of all the integers from n to 1. Ex: n! = 4x3x2x1 = 24

Question 32

Combinations

Answer 32

Give the number of ways x elements can be selected - from n elements. Order does not matter nCx n = total number of elements x = denotes the number of elements selected per selection n! / x! (n-x)!

Question 33

Permutations

Answer 33

The order of selection does matter. The number of permutations is always greater than or equal to the number of combinations. Total selections of x elements from n (different) elements in such a way that the order of selections is important. Can be called "arangements" nPx = n! / (n-x)!