Probability Models• Probability Model – the description of

some chance process that consists of two parts, a sample space S and a probability for each outcome.

• Tossing a coin – we know there are 2 possible outcomes–We believe that each outcome has a

probability of ½

• Sample space – a list of possible outcomes– Can be written using set notation S = { T, H }

Probability Notation• Probability models allow us to find the

probability of any collection of outcomes called an EVENT

• An event is a collection of outcomes from some chance process. (subset of sample space S notated as A, B, or C)

• P(A) denotes the probability that event A occurs

Probability of Events• Event A, sum of dice = 5, find P(A) =

• Event B, sum of dice not = 5, find P(B) =

• P(B) = P(not A)• Notice that P(A) + P(B) = 1

Probability of Events• Consider Event C = sum of dice = 6

• Probability of getting sum of 5 or 6? P(A or C) since these events have no outcomes in common… P(sum of 5 or sum of 6) = P(sum of 5) + P(sum of 6)

• P(A or C) = P(A) + P(C)

Basic Rules• Probability of any event is a number

between 0 & 1• All possible outcomes (options in a

sample space) must have probabilities that sum 1

• IF all outcomes in a sample space are equally likely, the probability that event occurs can be found using a formula: P(A) = number of outcomes corresponding to

event A total number of outcomes in sample space

Basic Rules• Probability that an event does not occur is

1 – (the probability that the event does occur).– The event that is “not A” is the complement of

A and is denoted by AC

• If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities.–When 2 events have no outcomes in common,

we refer to them as mutually exclusive or disjoint (no outcomes in common and never occur together)

Basic Rules• For any event A, 0 ≤ P(A) ≤ 1• If S is the sample space in a probability

model, P(S) = 1• In the case of equally likely outcomes:

P(A) = number of outcomes corresponding to event A total number of outcomes in sample space

• Complement rule: P(AC) = 1 – P(A)• Addition rule for mutually exclusive

events: If A and B are mutually exclusive, P(A or B) = P(A) + P(B)

Probability Models• Distance learning courses are rapidly gaining

popularity among college students. Here is randomly selected undergraduate students who are taking a distance-learning course for credit, and their student ages:

1. Show that this is a legitimate probability model.

2. Find the probability that the chose student is not in the traditional college age group (18-23 years).

Pg. 303

Age group (yr) 18 to 23 24 to 29 30 to 39 40 or over

Probability 0.57 0.17 0.14 0.12