What Are the Chances?

What Are the Chances? — page 3 — FINDING MATH IN RANDOMNESS IF YOU ARE FORCED TO DECIDE BETWEEN TWO SITUATIONS but aren’t sure which to choose you might do any number of things to narrow your options You might flip a coin you might roll a die or you might even play a game of eeny meeny miney moe People have used similar games of chance for thousands of years Members of ancient civiliza tions such as the Greeks Romans and Babylonians played such games However they were not involved in learning the math be hind those games Probability the study of how likely a given event is to occur did not come about un til the 1500s The math used for determining probability is not very challenging so it may seem odd that mathe maticians did not figure it out for so long They were definitely capable of doing the necessary calculations Many mathematicians of the an cient world were studying trigo nometry or algebra both topics that you cover in your later high school years So why did it take so long for mathematicians to dig in to proba bility In order to understand that it is important to understand what it means for an event to be ran dom When you think of random ness you probably think of events that you didn’t see com ing Mathematicians define random as ANCIENT ROMAN DICE GAMES WERE EVEN SHOWN IN THEIR MOSAIC ART 6

What Are the Chances? — page 4

What Are the Chances? — page 5 — Such attitudes kept mathematicians from understanding the random unable to be predicted for certain Mathematicians didn’t always think of randomness like this though For a long time until the 1500s many mathematicians believed that the attitude of the person rolling the dice influenced which numbers would appear They also believed strongly in luck and the idea of a higher power being in control of a particular event ness of an event However in the 1500s an Italian physician named Girolamo Cardano began to look at some of the math associated with rolling dice Cardano loved to gamble and study math He wrote a book based on some of his findings Liber de ludo aleae The book on games of chance despite being written in the mid-1500s was not published until 1663 Because the book was based on Cardano’s interest in gam bling it was not always taken seriously as a math text As a result French scholars Pierre de Fermat and Blaise Pascal are often considered the founders of modern probability thanks to the work they did in the 1650s They were not interested in shaking dice though They focused on how to divide the stakes or winnings of a game 8

What Are the Chances? — page 6 — That was the type of problem that interested Fermat and Pascal Imagine you and a friend are playing a game in which the winner will receive a 20 prize You are flipping a coin If the coin lands heads-up you get a point if it lands on tails your friend gets the point Unfortunately you aren’t able to finish the game before you have to go home If you win two rounds and your friend wins one how should you divide the prize Pascal looked at what might happen on the next flip He considered the chances that you would win the round and the game 3 1 In this case you would win the 20 and your friend would get nothing He compared that situation against the chances of your friend’s winning the round and the game finishing in a tie 2 2 If that were to occur you and your friend would each get 10 Because the chance of a tie is greater Pascal would have decided to give you 15 and your friend 5 Pascal and Fermat were able to solve many other problems in probabil ity They began to realize that although they could not predict what would happen they could predict the likelihood of its happening For instance in stead of saying with certainty that you would roll two sixes when you shook two dice they were able to tell the chances of your getting two sixes 3-1 2-2 P RO B A B I L I T Y 9

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