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Chapter 7: Probability
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probabilities. Finally, you will be introduced to some laws of probability
and how to compute conditional probabilities as well as determining whether
events are independent of each other.
7-2 Randomness and Uncertainty
Randomness
The term
randomness
suggests unpredictability. A simple example of
randomness is the random selection of an item from a production line in
which the item can be classified as a defective item or a non-defective item.
The outcome when the item is selected is unknown. The outcome could
either be a defective (
D
) item or a non-defective (
N
) item. Because the
classification outcome cannot be predicted for sure, we say it displays
randomness. This is an example of an easily describable random process.
However, other random processes can be quite intricate; for example, the
fluctuating prices of stocks are difficult to explain because there are so many
variables and combinations of variables that are influencing the prices.
Uncertainty
At some time or another, everyone will experience
uncertainty
. For
example, if you are playing a game of softball, and the pitch is on its way,
you may be uncertain as to whether to take a swing at the ball or not. Or
consider the case when you are approaching the traffic signals and the light
changes from green to yellow. You have to decide whether you can make it
through the intersection before the light turns red or not. You may be
uncertain as to what the correct decision should be.
Probability
When you ask yourself the question as to whether you believe that you can
make it through the yellow light before it turns red, the answer may be
“probably”. That is, you believe that you can make it across the intersection
before the light changes to red, but you still may have some doubt. The
concept of probability is used to quantify this measure of doubt. If you
believe that you have a 0.96 probability of getting across the intersection
before it turns red, you have made a clear statement about your doubt. The
probability statement provides a great deal of information, much more than