1. Definition of Probability
Section 7.2
Definition of Probability

2. Finding the Probability of an Event
The probability of an event occurring is a measure of the proportion of the time that the event will occur in the long run.
Finding the Probability of an Event
Suppose that in n trials an event E occurs m times. The relative frequency of the event E is m/n.
If the relative frequency approaches some value P(E) as n becomes larger, then P(E) is called the empirical probability of E.

3. Notice 150 total observations
Ex. The table below represents the frequency of certain types of license plates observed by a family on a recent trip. Find the probability distribution.
State
Number
Wisconsin 45
Illinois 80
Iowa 20
Indiana 5
Probability
45/150 = 0.300
80/150 = 0.533
20/150 = 0.133
5/150 = 0.033
Notice 150 total observations

4. Ex. Assume that when rolling a die each face is equally likely to show up. If event E = {2} then since S = {1, 2, 3, 4, 5, 6}, we have P(E) = 1/6. That is, the probability of rolling a 2 is 1 in 6.
Similarly, the probability of rolling any face number is 1/6.

5. Let S = {s1, s2, s3,…,sn} where each si represents a simple event (all mutually exclusive) and let P(si) represent the probability of event si.
The function P, which assigns a probability to each simple event is called a probability density function.
Also
probabilities are between 0 and 1
they add to 1
add probabilities

6. Finding the Probability of an Event E
Determine a sample space S associated with the experiment.
Assign probabilities to the simple events of S.
If E = {s1, s2, s3,…,sn} (each a simple event) then P(E) = P(s1) + P(s2) +…+ P(sn). If E is the empty set then P(E) = 0.

7. Ex. An experiment consists of spinning the hand on the disk below one time. Assume each outcome is equally likely. A C W
Find P(C) and then find
Notice S = {C, A, W} each of which has a probability of 1/3.