refresher

definition
Probability is the chance that an event will occur. It is measured by the ratio of the favorable cases to the total number of cases possible.

A bit of history: It is said that the creation of the theory of probability occurred in 1654 over a dice game gambling dispute between two famous mathematicians, Blaise Pascal and Pierre de Fermat. A few years later, the first book on probability, as it related to gambling, was published.

The subject of probability developed rapidly during the 18th century with the contributions of other famous mathematicians. Over the following centuries, probability theory grew and expanded into a general discipline known as measure theory.

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Ratios are used to show how likely, or unlikely, an outcome might be.
Such a ratio is called the probability.

For example, the probability of getting heads on the toss of a penny is the ratio lprobHalf. Heads is one of two possible outcomes when a penny is tossed.
penny

The ratio for probability can be expressed as:

defpossible

Ratios are most often expressed in the form of a fraction. Fractions, however, can also be expressed as decimals or percents. So probabilities may be expressed as fractions, decimals or percents.

ratiotriangle
As the chart on the left shows, probabilities range from 0 to 1.

If an event is impossible and will never occur, the probability is 0. 

If an event is absolutely certain to occur, the probability is 1. 

Otherwise, the value of a probability is between 0 and 1.
Events that are likely to occur have a probability greater than 0.50.
Events that are not likely to occur have a probability less than 0.50.

While probability was originally developed to deal with gaming techniques, it is used today in a wide range of applications. Even common sayings reflect the concept of probability.

Someone says "Don't hold your breath" when you are waiting for something to happen.  What is the person implying about the probability that the event will occur in the near future?
fish
ANSWER:  This statement implies that you may die holding your breath waiting for this event to occur.
Obviously, the probability of the event occurring in the near future, is extremely low, if not impossible.

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Example: A fair die is rolled and the outcome noted. Determine whether each of the following outcomes is: certain to happen,   certain not to happen,   likely to happen,   likely not to happen.

die
Possible rolls:
1, 2, 3, 4, 5, 6
• rolling a 2
• probability = 1/6  likely not to happen
• rolling a number less than 3
• probability = 1/6 + 1/6 = 2/6 likely not to happen
• rolling a 7
• not possible - certain not to happen
• rolling a number less than 10
certain to happen
• rolling a number greater than 1
• probability = 5/6   likely to happen
• rolling a factor of 6 (1,2,3,6)
• probability = 4/6   likely to happen
• rolling a number that is an integer
certain to happen
• rolling a negative number
certain not to happen


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