3. Probability Theory

Question 1

What is probability?

Answer 1

the proportion of times an event occurs when a random trial is repeated under the same conditions.

Question 2

What is random trial?

Answer 2

a process/experiment with 2+ possible outcomes were the occurrence cannot be predicted with certainty

Question 3

What is an outcome?

Answer 3

possible results of a trial

Question 4

What is an event?

Answer 4

an actual result of a trail from subset of possible outcomes

Question 5

What does ‘mutually exclusive’ mean?

Answer 5

When two events cannot occur at the same time

Question 6

What is a probability distribution?

Answer 6

the true relative frequency of all possible values of a discrete random variable

Question 7

What is a probability density function?

Answer 7

the true relative frequency of all possible values of a
continuous random variable

Question 8

What is the General Addition Rule for Probabilities and how do you use it?

Answer 8

P(A or B) = P(A) + P(B)
- if A and B are mutually exclusive

P(A or B) = P(A) + P(B) - P(A and B)
- if A and B are not mutually exclusive

Question 9

What does it mean if events are independent?

Answer 9

Occurrence of one event does not predict the occurrence of the second event

Question 10

What is the General Multiplication Rule and how do you use it?

Answer 10

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

• If A and B are independent then P(B|A) = P(B)

Question 11

How do you use a probability tree?

Answer 11

nodes are outcomes
branches are probabilities

add vertically
multiply horizontally

Question 12

What is the Law of Total Probability and how do you use it?

Answer 12

P(A) = ∑ P(B)P(A|B)
- B represents all the possble mutually exclusive values of conditions

example:
https://www.probabilitycourse.com/chapter1/1_4_2_total_probability.php#:~:text=Law%20of%20Total%20Probability%3A,)P(Bi).