Chapter 4

Question 1

Probability:

Answer 1

Probability: numerical value that measures the likelihood that an event occurs
p = 0 impossible
p = 1 definite

Question 2

Experiment:

Answer 2

Experiment: a process that leads to one of several possible outcomes

Question 3

Sample Space:

Answer 3

Sample Space: all possible outcomes in an experiment

Question 4

Event:

Answer 4

Event: a subset of outcomes of the experiment

Question 5

Mutually exclusive events:

Answer 5

Mutually exclusive events: no common outcomes

Question 6

Combining Events:

Answer 6

Combining Events:

• Union (A or B)
• Intersection (A and B - shared events)
• Complement (all outcomes not in the event A)

Question 7

Denote probability of any event A by:

Answer 7

P(A)
- between 0 and 1
- sum of all (mutually exclusive and exhaustive) = 1
IF YOU GOT OVER 1 YOU’RE WRONG

Question 8

Subjective Probability:

Answer 8

guess, belief, judgement

Question 9

Empirical Probability:

Answer 9

Empirical Probability: based on observed relative frequency

Question 10

Classical Probability:

Answer 10

Classical Probability: deduced from reasoning about the problem

Question 11

Law of Large Numbers:

Answer 11

LLN: The empirical probability approaches the classical probability if the experiment is run a very large number of times.

Question 12

Given odds from an event A occurring of “a to b”

Answer 12

P(A) = a/(a+b)

• you can convert odds to probabilities

Question 13

Conditional Probability:

Answer 13

Conditional Probability = P(A|B)

OR, P(B|A)

Question 14

Independent Events:

Answer 14

Independent Events:

if P(A|B) = P(A) or P(B|A) = P(B)

Otherwise, they are dependent. (when they give extra info about each other)

Question 15

The Multiplication Rule:

Answer 15

The Multiplication Rule: a way to find the probability of two events happening at the same time

General multiplication rule formula is: P(A ∩ B) = P(A) P(B|A) and the specific multiplication rule is P(A and B) = P(A) * P(B). P(B|A) means “the probability of A happening given that B has occurred”.

Question 16

Contingency Table:

Answer 16

Contingency Table: shows frequencies for two qualitative variables, where each cell represents a mutually exclusive combination of the pair

• can be converted to joint probability tables

Question 17

Total Probably Rule:

Answer 17

Total Probably Rule: expresses the probability of an event (A) in terms of probabilities of the intersection of A with mutually exclusive and exhaustive events

Question 18

Bayes’ Theorem - Posterior Probability:

Answer 18

Posterior Probability: can be found using the info on the prior probability P(B) along with the conditional probabilities

• is the revised or updated probability of an event occurring after taking into consideration new information.

Question 19

The values in the interior of the table represent the probabilities of the intersection of two events, also referred to as _____ probabilities.

Answer 19

The values in the interior of the table represent the probabilities of the intersection of two events, also referred to as joint probabilities.