


Historical Remarks
Games of chance, such as those involving dice, have been played for over 5,000 years. For almost that long, people have been trying to determine the odds or probability of winning at these games. Since the sixteenth century, mathematicians have been working steadily at this problem of calculating probabilities. Around 1620, Galileo wrote a paper on dice probabilities. However, the year 1654 is often considered as the beginning of probability theory. At that time that Blaise Pascal and Pierre Fermat began a correspondence on the subject.
Pierre Simon, the Marquis de Laplace, was an important contributor to probability theory. In 1812 he proved the central limit theorem which provides explains why so many data sets follow a distribution that is bellshaped, i.e., normally distributed. In Laplace’s book Analytical Theory of Probability, he writes:
We see that the theory of probability is at the bottom only common sense reduced to calculation; it makes us appreciate with exactitude what reasonable minds feel by a sort of instinct, often without being able to account for it … It is remarkable that this science, which originated in the consideration of games of chance, should become the most important object of human knowledge … The most important questions in life are, for the most part, really only problems of probability.
Click here to see the title page of Laplace's book.
A Classic Example
Probability is essentially an extension of the idea of a proportion, or ratio of a part to the whole. Let's look at a classic problem of drawing a colored ball out of an urn. Here the kind of urn we have in mind is a pottery vase, large enough to hold a number of colored balls and deep enough so that we cannot see what ball we select to draw out.
We need to discuss what the phrase "on average" means. In this case, after noting the color of the chosen ball, we put it back, mix well and select again. If we let Ng denote the number of green balls that we have obtained after performing this experiment N times, then we expect the ratio Ng / N to approach 0.6 as N becomes large. Similarly, we expect the likelihood of getting a red ball to approach 0.4. Here we say that the probability of selecting a green ball is 0.6 and that of selecting a red ball is 0.4.
Clicking below will bring up an applet that will allow you to perform the above experiment of selecting a ball from the urn containing 6 green balls and 4 red. Close the applet window when you are finished.



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