Probability-Nico

=Probability= Nico P.


 * History**

Probability is a branch of mathematics that deals with chance. It can be used in situations as basic as predicting the results of flipping a coin, to finding your chance of winning the lottery and how to increase that chance.

Probability studies started in earnest in the late 1600s, in attempts to analyze games of chance. These studies have been carried out by various people, some of the more notable including Pierre de Fermat, Blaise Pascal, and Gerolamo Cardano. It was in 1933 however when Andrey Nikolaevich Kolmoskov laid the foundations for modern probability theory, used today.

In this page I will be explaining about probability, what we in 8th grade should know about it, and several other useful things to know while using probability.

**Introduction**
The best place to start would be at the beginning. As mentioned earlier, probability is the study of chance. This means that you take some event, study and record it, and then examine the probability of that event occurring.

Probability is usually written in fractions, which can be converted to percents or ratios. The fraction is the easiest way to display the probability of something, because it shows all about the probability. The denominator of the fractions displays the total number of outcomes for that particular event. For example, if the problem was to write the probability of being chosen in one out of a thousand, the denominator would be 1000, because that is all the possible choices. The numerator of the fraction is the number of outcomes that involve whatever is being asked happening. As there is only one scenario where you would be picked, the numerator would be 1, making the fraction 1/1000. This can be converted into a ratio by saying that this will occur one in a thousand times, and a percent by dividing the numerator by the denominator. (In this case 0.001%)

**Application**
Let us apply this to a simple situation. You have put five different colored squares into a bag into which you cannot see, one red, one green, one blue, one yellow, and one pink. What is the probability that you will chose the red square on your first try? You would take the total number of possible outcomes, (Picking red, green, blue, yellow, or pink, therefore making 5 possibilities) and using that as the denominator. Then you see how many of these possibilities have you picking red from the bag. Of course, only one. Therefore the chance of you picking red from the bag is 1/5, 20%, or one in five.

To get more complicated, take flipping a coin, an example frequently used when describing probability. Suppose you want to know the probability of the coin landing on heads in one flip. Assuming that the coin is thrown into the air randomly with no interference, there is an equal chance of each side landing face up. How did I figure this out? I took the coin and examined it. The coin has two sides, meaning that there are only two possible outcomes. Either the coin lands on heads, or on tails. However, there is only one outcome per toss, which is either heads, or tails. Therefore the chance of the coin landing on heads is ½. This is derived from the one outcome heads represents, over the total possible outcomes. Then, taking ½ you convert it into a percent, which turns out to be 50%. This means that there is a 50% chance of the coin landing on heads in one throw, saying that theoretically there will be a heads about one in every two flips. This means there is an equal chance of the coin landing on heads as on tails, because the probability is 50/50.

Now, to make it more complicated say you wanted to know the probability of heads landing three times in seven flips. You use the same basic method. First you must find the denominator of the fraction, which is the total possible occurrences. You could do this by hand, using a **Counting Tree** or writing out all the possible outcomes but a simpler method is to use **Permutations**, something that is explained in the “Helpful Tools” section. Using the permutations you will find that there are 128 outcomes. This will make the denominator of the fraction. Then you must find the number of outcomes that have three heads in them. To do this you use another tool, **Pascal’s Triangle**, also explained in the tools section. Using the triangle, you find that there are 35 outcomes with 3 heads in them. Therefore the chance that there will be three heads in seven flips is 35/128, which is roughly 27%, which means that this occurrence will theoretically occur once every three attempts. That is a basic theory of probability as we 8th graders should know it. Most of the effort put into probability goes into trying to calculate all the possible outcomes in big numbers, or finding the numerator. Mostly it boils down to one simple thing: The denominator of the probability is the total number of outcomes in the given situation, and the numerator is the number of outcomes in which the situation applies.

Extra Links
Laws and Other Probability Things Useful Probability Tools