Download chapter 9: introducing probability

CHAPTER 9: INTRODUCING PROBABILITY
 Chance behavior is unpredictable in the short run, but has a regular and
predictable pattern in the long run.
 Flip a coin. What is the probability that the coin comes up heads?
o Classical probability – assume all outcomes are equally likely
o Count Buffon (1707-1788) 2048/4040 = .5069
o Karl Pearson (1900) 12,012/24,000 = .5005
o John Kerrich 5067/10,000 = .5067
 Random – individual outcomes are uncertain but there is a nonetheless
regular distribution of outcomes in large numbers of repetitions
 Probability – proportion of times the outcome would occur in a very long
series of repetitions
o Trials must be independent
o Probability is empirical
o Computer simulations
 Probability models
o Sample space (S) – set of all possible outcomes
o Event (E) is an outcome or set of outcomes (subset of S)
o Probability model consists of a sample space and a way of
assigning probabilities to events
 Probability Rules
o 0 ≤ P(E) ≤ 1
o Sum of all probabilities = 1
o Complement Rule: P(E) + P(E’) = 1
o Addition Rule for Disjoint Events

P(A or B) = P(A) + P(B)
Example: Two fair dice are rolled. Calculate the following probabilities.
1. Doubles are rolled
2. A sum of six is rolled
3. A sum of seven or nine is rolled
4. The sum of the digits is odd
 Normal Probability Models
o Normal distributions are probability models
o Example: Suppose the heights of American women are distributed
N(64, 2.7).

What proportion of women are more than 68 inches tall?

What is the probability that a randomly chosen woman is
more than 68 inches tall?
 Random Variables
o Variable whose value is a numerical outcome of a random
phenomenon
o Can be discrete or continuous
 Probability Distribution
o Tells what values a random variable X can take and how to assign
probabilities to those values
 Personal Probability – expresses an individual’s judgment of how likely an
outcome is