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| Used with permission from MathFunny.com |
Math and I have never been the best of friends, especially during times when probabilities and/or statistics are involved. But the information we've been going over in class the last couple of weeks has helped to make me (albeit, a very small amount) more confident.
How Probabilities are Determined
We begin with the basics: vocabulary terms. Often the definition of words change depending upon what field you are using them in; things that have one meaning in layman's terms will have a completely different meaning in science, math, and especially law. Math is like another language entirely, and studying it is essentially learning the definitions of each word or equation. Each formula, equation, etc., has its' own definition which tells you what it means and how to properly use it.
- Experiment - An activity in which results can be observed and recorded.
- Outcome - Each of the possible results of an experiment. (Ex.: With coins the outcome is heads or tails)
- Sample Space - A set of all possible outcomes for an experiment. Results such as S = (H,T) can be modeled by a tree diagram, which we will look at later.
- Event - Any subset of a sample space, such as the event of dice; an example of this would beS = (2, 4, 6) where the sample space for S is rolling a standard die with even numbers as the outcome.
When determining probability, there is Experimental (or empirical), and Theoretical. the difference between the two is that experimental is what you actually observe while theoretical is what would happen under perfect and ideal conditions. Additionally, we believe in and try to abide by Bernoulli's Theorem which states that if an experiment is repeated enough times that the empirical probability will become closer to the theoretical probability. Sort of like the whole monkeys and typewriters idea.
We encounter from time to time events that are impossible or certain. These are represented in an equation as 0 and 1, respectively. If something is equally as likely to happen as another option, we often describe that as being a 50/50 chance or probability, however we would write that as a 1/2 probability. Events can also be mutually exclusive or complementary. With mutually exclusive events if one thing happens the other cannot, OR they are mutually exclusive if the events have no elements in common. Complementary events are along the lines of: Chance of rain = 25%, so the chance of no rain is 100% - 25% = 75% or 3/4 probability of no rain.
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| On a somewhat related note, the probability of many home owners in the Phoenix Metro Area getting flood insurance after this weeks crazy, valley-wide flooding is very high. Image courtesy of the Associated Press & BBC World News |
The following websites do a much better job at explaining introductory probability than I do:
Love the car picture, it is a rare occasion for Arizona.
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