1. Chapter 10 - Introducing Probability
Probability: The mathematics of chance behavior.
Probability Vocab
Random = individual outcomes are uncertain, but a large number of repetitions produces a regular distribution.
Probability = The proportion of times an outcome would occur in a long series of repetitions.
Probability Theory = The branch of mathematics that describes random behavior.
Probability Factoids:
Any probability is a number between 0 and 1.
All possible outcomes together MUST have a total probability equaling 1.
The probability that an event does NOT occur = 1- the probability that it DOES occur.

2. If 2 events have no outcomes in common, the probability that one OR the other occurs = the SUM of their individual probabilities…
ex: Blood Type (Afr. American distribution)
Type O A B AB
Probability ?
What is the probability that the person chosen has either type A or type B blood?
( ) = .47
What is the probability of type AB blood?
( ) = > ( ) = .04

3. Probability Models
Random Variable = A variable whose value is a numerical outcome of a random phenomenon.
Probability Model/Distribution = Describes what the possible values of a variable are and the probabilities assigned to those values.
2 requirements:
a) Every probability in the distribution must be a number between 0 and 1.
b) The sum of the probabilities in the distribution must =1.
Sample space (S) = The set of all possible outcomes.
Event = An outcome or set of outcomes from the sample space.
ex: Coin toss: Sample space is S = {H, T} / Event = Toss a head
ex: Roll 2 Dice: Sample space (S) =
Event = “Roll a 5”
= (1, 4), (2, 3), (3, 2), (4, 1)
= 4/36 outcomes =1/9
36 possible
outcomes

4. Probability Model Types
Finite: Fixed and limited number of outcomes.
Continuous: Outcomes may take on any value in an interval of numbers.
Finite Probability Model example:
Student’s grade on a 4.0 scale (A = 4.0)
X is the random variable representing the grade of a student chosen at random:
Grade
Probability
Probabilities add to 1
The probability that a student got a B or better is expressed as:
P(X > 3) = P(X = 3) + P(X = 4)
= = .45

5. P(X) = Area of shaded region
Continuous Probability Model
The probability dist. of X is described by a density curve.
X is defined as an interval of values rather than just one value.
The probability of any one single value = 0.
P(X) = Area of the interval under the density curve.
ex:
P(X) = Area of shaded region

6. Normal Curves
Normal distributions ARE probability distributions
Heights of young women ex: X = height of random woman yrs old (in inches)
X has distribution N(64.5, 2.5)
What is the prob. that a randomly chosen young woman is between 68 and 70 inches tall?
P(68 < X < 70) =