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قطعة العشوائية

(1) Randomness and uncertainty exist in our daily lives as well as in every
discipline in science, engineering, and technology. Probability theory is a
mathematical framework that allows us to describe and analyze random
phenomena in the world around us. By random phenomena, we mean
events or experiments whose 11 outcomes we can't predict with certainty.


(2) Let's consider a couple of specific applications of probability in order to
get some intuition. First, let's think more carefully about what we mean by
the term’s "randomness" and "probability" in the context of one of the
simplest possible random experiments: flipping a fair coin.

3) One way of thinking about "randomness" is that it's a way of
expressing what we don't know. Perhaps if we knew more about the force,
I flipped the coin with, the initial orientation of the coin, the impact point
between my finger and the coin, the turbulence in the air, the surface
smoothness of the table the coin lands on, the material characteristics of
the coin and the table, and so on, we would be able to definitively say
whether the coin would come up heads or tails. However, in the absence of
all that information, we cannot predict the outcome of the coin flip. When
we say that something is random, we are saying that our knowledge about
the outcome is limited, so we can't be certain what will happen.


(4) Since the coin is fair, if we don't know anything about how it was
flipped, the probability that it will come up heads is 50%, or 12. What
exactly do we mean by this? There are two common interpretations of the
word "probability." One is in terms of relative frequency. In other words, if
we flip the coin a very large number of times, it will come up heads about
12 of the time. As the number of coin flips increases, the proportion that
come up heads will tend to get closer and closer to 12. In fact, this intuitive
understanding of probability is a special case of the law of large numbers,
which we will state and prove formally in later chapters of the book.


(5) A second interpretation of probability is that it is a quantification of our
degree of subjective personal belief that something will happen. To get a
sense of what we mean by this, it may be helpful to consider a second
example: predicting the weather. When we think about the chances that it
will rain today, we consider things like whether there are clouds in the sky
and the humidity. However, the beliefs that we form based on these factors
may vary from person to person - different people may make different
estimates of the probability that it will rain. Often these two
interpretations of probability coincide - for instance, we may base our
personal beliefs about the chance that it will rain on an assessment of the
relative frequency of rain on days with conditions like today.


(6) The beauty of probability theory is that it is applicable regardless of the
interpretation of probability that we use (i.e., in terms of long-run
frequency or degree of belief). Probability theory provides a solid
framework to study random phenomena. It starts by assuming axioms of
probability, and then building the entire theory using mathematical
arguments.

قطعة حريق هائل

1) Over the roar of the fire, Mike heard Ben shout, "Hurry! The fire is
almost on us!" Mike's arms were sore and tired, but he swung his axe even
faster. He didn't even stop to wipe the tears from his stinging eyes. The
greedy fire kept coming. The more the fire destroyed, the more it wanted.
Mike worked shoulder to shoulder with the other smokejumpers to build a
firebreak. His only thought was to stop the flaming monster that was
raging through the forest.


(2) At last, the smokejumpers finished the firebreak. If the fire were
powerful enough, it would jump over the firebreak that they had worked so
hard to make. Then they would have to start all over again. Mike stood
motionless, his face black with ash, his shirt wet with sweat. He was too
exhausted to move because he had given all of himself to fighting the fire.
He turned his head and noticed Ben watching him.


(3) Suddenly all that Ben had taught Mike about proving his bravery was
clear. A man was not brave if he did something just to prove his courage.
He was brave only when he forgot about himself. Today Mike had showed
that he cared very much about the others with whom he was working.

قطعة الحرب الباردة

(1) Starting with major scientific breakthroughs during the 1930's,
countries have developed weapons that are based on nuclear energy. The
use of nuclear weapons reached its height with the outbreak of World War
II and the Cold War. Two of the world's major superpowers, the USA and
Soviet Union, threatened each other with the use of nuclear weapons,
which was referred to as the Cold War.


(2) Although relations between the Soviet Union and the United States had
been strained in the years before World War II, the U.S.-Soviet alliance of
1941-1945 was marked by a great degree of cooperation and was essential
to securing the defeat of Nazi Germany. As late as 1939, it seemed highly
improbable that the United States and the Soviet Union would forge an
alliance. U.S.-Soviet relations had soured significantly following Stalin’s
decision to sign a non-aggression pact with Nazi Germany in August of
1939. In spite of intense pressure to sever relations with the Soviet Union,
Roosevelt never lost sight of the fact that Nazi Germany, not the Soviet
Union, posed the greatest threat to world peace. In order to defeat that
threat, Roosevelt confided that he “would hold hands with the devil” if
necessary. Finally, two devastating atomic bomb attacks against Japan by
the United States, coupled with the Soviets’ decision to break their
neutrality pact with Japan by invading Manc1huria, finally led to the end of
the war in the Pacific. Soon after the war, the alliance between the United
States and the Soviet Union began to unravel as the two nations faced
complex post- war decisions


(3) At various conferences, the most important of which were at Yalta and
Potsdam, the three powers split Germany and its capital Berlin in two, with
the eastern portion controlled by the Soviet Union and the western portion
controlled jointly by the United States, the United Kingdom, and France.
Additionally, the Soviet Union was given influence over the governments of
several Eastern European states, where they promptly set up loyal,
communist puppet regimes.


(4) The United States and the West feared the creation of this Eastern Bloc,
as Western journalists and government termed it, and the further spread of communism and/or totalitarian states in the rest of the world. U.S. foreign
policy became one of containment - essentially, stopping the spread of
communism wherever it could. This was in direct opposition to the Soviet
Union's policy of fostering the spread of communism, especially in its Asian
neighbors. The Americans then feared that the USSR/ Communist influence
that already spread over Eastern Europe, would influence the democracies
of western Europe.

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