3. Sample Spaces and Events

Question 1

what is subjective probability?

Answer 1

the probability of an event is the way someone expresses their degree of belief the event will occur, based on their judgement, and given the evidence they have seen, measured on a scale from 0 to 1

Question 2

what is classical probability?

Answer 2

when there a finite number of equally likely outcomes, the probability of an event is the proportion of those outcomes that correspond to an event occuring

Question 3

what is frequentist probability?

Answer 3

in a repeated experiment, the probability of an event is its long-run frequency

Question 4

what is mathematical probability?

Answer 4

a function that assigns to each event a number between 0 and 1, where that function has to obey axioms

Question 5

what is meant by a sample space?

Answer 5

the set of all possible outcomes, given the letter Ω

Question 6

what is meant by a sample outcome?

Answer 6

one of the possible outcomes, given the letter ω

Question 7

what is meant by an event?

Answer 7

a set of sample outcomes, or in other words, a subset of the sample space

Question 8

what are the distributive laws for events?

Answer 8

you can multiply out brackets with events

A∩(B∪C) = (A∩B)∪(A∩C)
A∪(B∩C) = (A∪B)∩(A∪C)

Question 9

what are De Morgan’s laws

Answer 9

(A∩B)^c = A^c ∪ B^c
(A∪B)^c = A^c ∩ B^c