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WEEK 4: DATA FOR TWO VARIABLES AND PROBABILITY (PART 2)
Business managers frequently face uncertain situations and have to base
their decisions on an analysis of uncertainties. For example, what is the
likelihood that the project can be completed by the due date? What is the
chance a new assembly method will increase productivity? What are the
odds a new investment will be profitable? To analyze uncertainties to
answer these questions, you need to know some basic probability
concepts. But first, let's cover some probability definitions.
BASIC PROBABILITY CONCEPTS
Probability is a measure of the chance that a certain event will occur and is
measured on a scale from 0 to 1.
A probability value of 0 indicates that the
event cannot happen, and a probability value of 1 reveals that the event is
sure to happen.
A process that results in one of a number of well-defined outcomes that
cannot be predicted in advance is called an experiment (random
experiment).
The listing of all possible outcomes of a random experiment
is referred to as the sample space.
Any subset of a sample space is called
a random event.

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ASSIGNING PROBABILITIES
Once an event is defined, a probability can be assigned to it. Three
approaches of assigning probabilities that are most frequently used are
classical, relative frequency, and subjective methods.
Classical Method:
Classical method is appropriate when all the possible outcomes of an
experiment are
equally likely
to occur. This type of probabilities is classical
probability. For example, considering the experiment of rolling a six sided
die, it is seasonal to say the six outcomes are equally likely.
So if an event is defined as observing even numbers,
p(event numbers)=3/6=0.5

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Relative Frequency Method:
When data are available to estimate the proportion of the time the
experimental outcome will occur of the experiment is repeated a large
number of times, the relative frequency method (also called empirical
probability) is appropriate. This method of assigning probabilities based on
experimentation or historical data.
This type of probabilities is also called
empirical probability. For example, the study of waiting times in the X-ray
department for a local hospital shows the number of patients waiting for
service on 20 successive days (shown in the following table):
Number
Waiting
Number of Days
Outcome Occurred
Probability
0
2
2/20=0.1
1
5
0.25
2
6
0.30
3
4
0.20
4
3
0.15
Total
20
1.00
Using the relatively frequency method, the probability of each outcome
(number of waiting 0, 1,2,3,4) can be obtained (see the last column of the
above table). Then we can figure out probability of union events.
P(more than 2 waiting)=P(3 or 4 waiting)=p(s) +p(4) =0.20+0.15=0.35
Subjective Method:
When one cannot realistically assume that the outcomes are equally likely
and when little relevant data are available, i.e. both classical and relative
frequency methods are not appropriate, subjective method should be used.