This document provides an overview of key concepts in probability models, including: 1. A probability model consists of a sample space (the set of all possible outcomes) and probabilities assigned to each outcome. Common examples are coin tosses and dice rolls. 2. Events are subsets of outcomes from the sample space. The probability of an event, written P(A), is the chance it occurs. 3. For mutually exclusive events like getting a sum of 5 or 6 on dice, the total probability is the sum of the individual probabilities. Basic rules of probability include that all probabilities must sum to 1 and the probability of an event's complement is 1 minus the original probability.

1. 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 }

2. 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

3. 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

4. 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)

5. 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

6. 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

7. 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)

8. 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:
Age group (yr)
18 to 23
24 to 29
30 to 39
40 or over
Probability
0.57
0.17
0.14
0.12
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).
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