3.1: Conditional and Joint Probabilities

Question 1

Probability is a number between..

Answer 1

0 and 1 that describes a chance of a stated event occurring.

Question 2

Priori probability is one based on…

Answer 2

Logical analysis and data that is known.

Question 3

Objective probability is?

Answer 3

Probability that does not vary from person to person.

Question 4

Dutch Book Theorem is a result in probability theory stating that..?

Answer 4

Inconsistent probabilities create profit opportunities.

Question 5

The sum of the probabilities of any set of mutually exclusive and exhaustive events equals to?

Answer 5

1

Question 6

The probability of any event E is a number between 0 and 1:

Answer 6

0 ≤ P(E) ≤ 1.

Question 7

Calculation of odds for Pe = ?

Odds against e = ?

Answer 7

[1 - Pe]

[ 1 - Pe] / Pe

Question 8

Addition Rule for Probabilities is the probability of..?

and is calculated as:

Answer 8

A and B both occurring.

P(A or B) = P(A) + P(B) – P(AB)

Question 9

Multiplication Rule for Independent Events states that when two events are..

Calculated as?

Answer 9

Independent, the joint probability of A and B equals the product of the individual probabilities of A and B.

P(AB) = P(A)P(B)

Question 10

What does the Total Probability Rule explain?

Answer 10

This rule explains the unconditional probability of the event in terms of probabilities conditional on the scenarios.

Question 11

What does S and Sc mean?

Answer 11

S = scenario,

Sc (complement) = opposite of the scenario occurring.

Question 12

P(S) + P(SC) = ?

Answer 12

1, as either S or not-S must occur.

Question 13

The Probability Rule formula for 2 Scenarios:
P(A) = …

Answer 13

P(A) = P(AS)+P(ASc) = P(A/S)P(S) + P(A/Sc)P(Sc)

Question 14

The Probability Rule formula for N Scenarios:

Answer 14

P(A) = P(AS1)+P(AS2)+…+P(ASn) = P(A/S1)P(S1) + P(A/S2)P(S2)+…+P(A/Sn)*P(Sn)