Bayes & Probability

Question 1

What is independence?

Answer 1

The occurrence of one event doesn’t affect the occurrence of another

Question 2

Define mutually exclusive

Answer 2

Two events cannot occur at the same time

The occurrence of one event means the other event does not occur

Question 3

Explain the Law of Addition

Answer 3

Add probabilities of MUTUALLY EXCLUSIVE events

“OR”

Example: male or female child
(1/2 + 1/2 = 1)

Question 4

Explain the Law of Multiplication

Answer 4

Multiply probabilities of INDEPENDENT events

“AND”

Example: The probability that a couple has 2 female children (1/2 x 1/2 = 1/4)

Question 5

What is a binomial distribution?

Answer 5

The probability of a certain number of events occurring in a certain number of independent trials
- order doesn’t matter

• Each trial has a “success” or “failure”

Equation:

P = (n!/(n-r)! r!) (p^r * q^n-r)

n= total sample size
r= # of events of interest (“successes”) occuring
p= probability of “success”
q= probability of “failure”
! = factorial (4!= 4x3x2x1)

Question 6

What is Bayes Theorem?

Answer 6

Method for considering all possibilities or events

Equation:
P(C) * P(O|C) / [P(C) * P(O|C)] + [P(NC) * P(O|NC)]

P(C) - Probability of C occurring
P(O|C) - Probability of observation O if C occurs
[P(C) * P(O|C)] - Joint probability of seeing observation O if C occurs AND C occuring
[P(NC) * P(O|NC)] - Joint probability of observation O if NC occurs AND NC occurring