Are We Civilized Essays - Democracy, Elections, Cherokee Nation

Are we civilized? We are starting to witness the beginning of a new era. It is full of information and technology, and it will decide how the future is going to be. But despite all our new inventions and ideas that show us how we're better off than the generations before us, have we grown in any other ways? Does being civilized only mean to become more advanced technologically, or does it apply to our moral foundation? It is very obvious that society has developed a lot in learning and technology. Today, we have inventions such as the stealth fighter, the home computer and nuclear powered power plants and naval vessels. Things that were imagined many years back have now become today's reality. Single machines now hold the jobs that used to take hundreds of men to accomplish by hand, so in this sense, we have become more civilized. On the other hand, not all of the inventions that have been developed from the technology world are used to do good deeds. Our great society has allowed the production of many weapons whose sole intention is to create mass destruction and to kill large amounts of life. Many people now live in constant fear of the use of these weapons, while others sit back and enjoy them for protection. We still have as many wars as we did in the past, but now the new technology used in them helps bring about more human casualties. An example of this would be Operation Desert Storm. I was a 23-year-old man, sent off to fight for the liberation of Kuwait and to kick the crap out of a bully named Saddam Hussein. I was the crewchief on an UH-60 Blackhawk helicopter assigned to the 1st Cavalry Division from Ft. Hood, TX. From the time the air war started to the 100 hours of hell we threw at the Iraqi Army, it was never more evident the role that technology played in decimating an enemy and b! reaking his will to win and survive. The pictures that my young eyes saw will forever be burned into memory. Technology was a teacher of pain and suffering, but it was also a savior in helping bring home the lives of many young men who might of not come back in previous wars. Besides the wars, society really has yet to understand other people. Prejudice is alive and burning in the hearts of many throughout our society. Many hate groups are still around today, as they were hundreds of years ago, and many new groups are starting to form and become active. Oklahoma City felt the wrath of some very passionate people who were trying to avenge the loss of comrades to the Federal Government. Many innocent people were killed, and it all boils down to beliefs and ideas. Racism still has its hand around the throats of many in our society as well. It seems that some of the worst racists in our society are the ones who say they're not racist, but on the inside they really are. These are the people who say they're not racist, but they don't hire the East Indian employee who was the most qualified of the candidates. They coach the all white basketball team. They fight over the red and blue colors of bandannas worn around their heads. The worst part is, it d! oesn't even phase them when they are doing it. In the past when our country was just starting to be formed, there were many prejudices just because people were different. Now over a century later, people haven't changed much, which makes me wonder if we really have become civilized yet. Democracy is also something that has played a big part in our journey to become civilized. A democracy in my words is where the people who choose to live under it run the government. And to have a true democracy, everyone must vote! People vote to exercise their democratic rights. If only 70% vote, then 70% control 100% of the government. Voting without adequate understanding and choosing candidates for the wrong reasons are symptoms of voting for the sake of voting and not taking an active interest

How to Prove the Complement Rule in Probability

How to Prove the Complement Rule in Probability Several theorems in probability can be deduced from the axioms of probability. These theorems can be applied to calculate probabilities that we may desire to know. One such result is known as the complement rule. This statement allows us to calculate the probability of an event A by knowing the probability of the complement AC. After stating the complement rule, we will see how this result can be proved. The Complement Rule The complement of the event A is denoted by AC. The complement of A is the set of all elements in the universal set, or sample space S, that are not elements of the set A. The complement rule is expressed by the following equation: P(AC) 1 – P(A) Here we see that the probability of an event and the probability of its complement must sum to 1. Proof of the Complement Rule To prove the complement rule, we begin with the axioms of probability. These statements are assumed without proof. We will see that they can be systematically used to prove our statement concerning the probability of the complement of an event. The first axiom of probability is that the probability of any event is a nonnegative real number.The second axiom of probability is that the probability of the entire sample space S is one. Symbolically we write P(S) 1.The third axiom of probability states that If A and B are mutually exclusive ( meaning that they have an empty intersection), then we state the probability of the union of these events as P(A U B ) P(A) P(B). For the complement rule, we will not need to use the first axiom in the list above. To prove our statement we consider the events Aand AC. From set theory, we know that these two sets have empty intersection. This is because an element cannot simultaneously be in both A and not in A. Since there is an empty intersection, these two sets are mutually exclusive. The union of the two events A and AC are also important. These constitute exhaustive events, meaning that the union of these events is all of the sample space S. These facts, combined with the axioms give us the equation 1 P(S) P(A U AC) P(A) P(AC) . The first equality is due to the second probability axiom. The second equality is because the events A and AC are exhaustive. The third equality is because of the third probability axiom. The above equation can be rearranged into the form that we stated above. All that we must do is subtract the probability of A from both sides of the equation. Thus 1 P(A) P(AC) becomes the equation P(AC) 1 – P(A). Of course, we could also express the rule by stating that: P(A) 1 – P(AC). All three of these equations are equivalent ways of saying the same thing. We see from this proof how just two axioms and some set theory go a long way to help us prove new statements concerning probability.