The Classical Interpretation Of Probability

Question 1

What is the classical interpretation of probability in general?

Answer 1

All outcomes of an experiment are equal

Question 2

Define the classical interpretation of probability

Answer 2

Question 3

What equation explains everything about the classical interpretation of probability

Answer 3

Question 4

What is the theorem in Multiplication principle?

Answer 4

Question 5

What is the proof behind the theorem in multiplication principle?

Answer 5

Induction by using the assumption to reduce the argument down to the basis step

Question 6

What is a permutation?

Answer 6

An ordered arrangement of objects

Question 7

How can you prove the sampling with replacement expression?

Answer 7

Follows from the theorem in multiplication principle

Question 8

Define a factorial

Answer 8

Question 9

What is a combination?

Answer 9

An unordered arrangement of objects

Question 10

Explain the expression for n choose r

Answer 10

We use the expression from earlier and divide by r! because each unordered permutation occurs r! times

Question 11

What exactly is C(n,r)

Answer 11

n choose r the different ways of choosing r distinct elements from a set of n distinct elements

Question 12

Explain the logic behind ordered choice with replacement?

Answer 12

The total n of elements that we choose is r
The total number of timed that we to move category (to pick something else) is n-1

But this is kind of irrelevant as we need to to n-1+r things anyway. So in the C(n,r) formular let n=n-1+r

Question 13

State the summarise table

Answer 13

Question 14

What happens if you are doing permutations but elements aren’t distinct?

Answer 14

You need to subtract the number of repeats.
This will usually be very nice numbers and can be done through division eg with 2 similar elements (both being selected) you just divide by 2

Question 15

Classical probability of probability
Aka

Answer 15

Counting argument