Discrete Probability

Question 1

What is the sample space?

Answer 1

The set of all possible outcomes of an experiment

Question 2

What is the size of the sample space?

Answer 2

The amount of possible outcomes - e.g. 4 for flipping a coin twice.

Question 3

What is P(A U notA)?

Answer 3

1, as it is P(omega)

Question 4

What is a finite discrete probability space?

Answer 4

(omega, P) - a finite set of outcomes w, called a sample space, omega, with a function P: omega -> R mapping the outcomes to a real number.

Question 5

What is P(A∩B) for independent events in a finite discrete prob. space?

Answer 5

P(A)P(B) assuming independence.

Question 6

What is the general formula for P(AUB)?

Answer 6

P(A U B) = P(A) + P(B) - P(A ∩ B)

Question 7

What does P(B|A) mean?

Answer 7

The probability of B happening given that A has already occurred. P(A) != 0

Question 8

What is the formula for P(B|A)?

Answer 8

P(B|A) = P(B ∩ A) / P(A)

Question 9

What is Bayes’ formula?

Answer 9

P(B|A) = P(A|B)P(B) / P(A)

Question 10

What is the expansion of Bayes’ rule?

Answer 10

P(B|A) = P(A|B)P(B) / (P(A|B)P(B) + P(A|notB)P(notB))

Question 11

How can Bayes’ rule prove independence?

Answer 11

A and B are independent if any of these three hold:
P(A∩B) = P(A)P(B)
P(B|A) = P(B)
P(A|B) = P(A)