Pascal's Triangle and the Theory of Probability

Probability affects almost everything we do. Probability is the effect or outcome of an event. In real life probability can be the difference from you winning the lottery to buying a defective item at the grocery store. Pascal's triangle, which was created by Blaise Pascal, can be used to predict probability.

Pascal's triangle is named in the honor of Blaise Pascal. Although others have constructed the same triangle before the triangle was named after him. Blaise Pascal showed brilliant talent from the very beginning. . (Giancoli, D., C p.276) Pascal's triangle is a tool to calculate probability. Blaise Pascal's surname is used as a measurement of pressure. (Benson, J. p.379)

Pascal's triangle is used in calculating probability. Pascal's triangle in constructed by adding the numbers adjecent to the preceding rows. For example in the 2^nd row the numbers are 1 2 1 and to find the 3^rd row you would add 1+0=1, 1+2=3, 2+1=3, 1+0=1 and the third row is 1 3 3 1. In this way Pascal's triangle can calculate probability. First you have to calculate the row of Pascal's triangle. (Fendel, D. p.450)You can calculate the probability by using the row of Pascal's triangle with the number of attempts that you are going to do the event. For example if I were going to attempt to pick a ticket for a raffle out 5 tickets then I would use the 5^th row of Pascal's triangle. The 5^th row of Pascal's triangle is 1 5 10 10 5 1. If we use the formula nCr which means that we are selecting a number of r from a total number of n. in this case we are attempting to pick a raffle ticket or in other words 1 number from a total of 5 numbers.(Fendel, D. p. 458) There is 1 way that I could pick no tickets from 5 tickets or in other words 5C0, there are 5 ways I could pick 1 ticket which is 5C1, there are 10 ways I could pick 2 tikcets from 5 tickets which is 5C2, there are 10 ways that I could pick 3 tickets from 5 tickets which is 5C3, there are 5 ways that I could pick 4 tickets from 5 tickets which is 5C4, and there is 1 way that I could pick 5 tickets out of 5 tickets which is 5C5.