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PROBABILITY
At the present time probability has become an acceptable part of mathematics.
In ordinary language the probability of an event means the likelihood of its occurence, and mathematical probability defines an exact measurement of this by assigning values from 0 to 1. Thus if an event is impossible, its probability equals 0; and if it is absolutely certain, its probability equals 1. If it is neither impossible nor absolutely certain, then its probability has some value between 0 and 1.
A die has 6 faces indicating the numbers from 1 to 6. The probability of throwing a 7 with one throw of 1 die equals 0 since this cannot happen. The probability that the number thrown is less than 7 equals 1, since this cannot fail (assuming ordinary conditions such that some face must come up).
Suppose an honest player throws an unloaded die. What is the probability of number 3 coming up? Since there are 6 ways the die can come up and, of these 6 ways, exactly 1 way is for number 3 to come up, we say that the probability of throwing a 3 is 1/6. Here we note that there is one way in which this event can happen and 5 ways it can fail and that all 6 ways are equally likely.
Under such circumstances probability is measured as follows: If an event can happen in h ways and can fail in f ways (all equally likely) then the probability that it will happen is given by
The probability that it will fail is given by
Since the
event must certainly either happen or fail, the probability of its
either happening or failing must equal 1. In accordance with this, we
see that p+q=1. Thus, the probability of throwing a 3 was
so
the Probability of not throwing a 3 must be
Two events are mutually exclusive if they cannot both happen (under some specified conditions). Thus, when a coin is tossed once, "heads" and "tails" are mutually exclusive events.
Events which cannot affect each other in any way are called independent events. Thus the heads or tails that comes up with any particular toss of a coin is not influenced in any way by the results of previous tosses.
If the occurence of event a affects the probability of event b, then b is said to be dependent on a.
Suppose I draw out one card at random from an ordinary pack, keep this card and then draw a second card. What I draw first will affect the probabilities in regard to the second card drawn.
HEALTH AND PHYSICAL EDUCATION
Physical Education teachers also called gym teachers or P.E. teachers - play an important educational role by instructing students of all ages in physical fitness and well-being. They also play a big role in our childhood, during our school life, all the way from Kindergarten through the last grade.
Good P.E. teachers should have a very positive effect on the physical fitness, attitude and health of children. In the USA there is a President's Council on Physical Fitness and Sports which sets the standard for America's kids: "the ability to last, to bear up, to withstand stress, and to live under difficult circumstances where an unfit person would be ineffective or would quit."
The emphasis these days is lower on the win-or-lose outcome, and more on what play is supposed to be about - having fun! Kids like to be active, for a few minutes at a time. Showing them how to stay active for 15 minutes at a time teaches them lots of things, including new skills and abilities, and helps them get fit at the same time.
The most important thing is that a teacher should help the kids to work towards their personal goals according to their abilities. They should improve their skills and learn to do something that they were unable to do before. For example if a child was unable to do a handstand and she learned it that is his/her success. That is what makes them feel better and more self-confident.
In the United States a Bachelor's Degree in Physical Education is the minimum for most P.E. teacher positions, and a Master's Degree is often required. Teachers must also hold a state Certification for public K-12 schools. Students who are going to be PE teachers can specialize in health promotion or exercise science.
Before graduating, future physical education teachers must finish at least one semester of student teaching and pass the Praxis I and II exams. Also, some states and colleges require physical education teachers to pass a comprehensive test before they are licensed. A good example is the California Subject Examination for Teachers (CSET), but each state will have its own testing requirements.
Future teachers of physical education may want to join groups and organizations to help develop physical education standards, such as the American Alliance for Health, Physical Education, Recreation and Dance, which aims to enhance the profession by providing opportunities for growth and development. They can also gain experience teaching young people by working as a coach or volunteer. This type of experience will look good on a resume while job hunting.
There are some states and school districts that require new teachers to complete their master's degree in education within a certain period of time after employment. A master's degree in physical education or a relevant field can also lead to a higher salary.
One of the positive sides of the job is being around kids to teach them the benefits of being physically active. It is great to see children succeed. Also, it was nice to hear good things from parents about the positive influence you have on their children through your teaching.
Graduates with a Bachelor of Science (B.S.) degree in Health and Physical Education typically find jobs as health teachers and physical education teachers in grades kindergarten through 12, or as coaches for any educational level, including college. Others manage or work in health clubs, correctional institutions, camp programs, sports management, professional sports and recreation programs. Some pursue certification in athletic training.
GRAVITATION
Gravitation is a very important force in the universe. Every object has a gravitational pull which is like magnetism. But, unlike magnetism, gravitation is not only in iron and steel. It is in every object large or small; but large objects, such as earth, have a stronger pull than small ones.
Isaac Newton, the great scientist of the seventeenth century, first studied gravitation. When he was u boy he often saw how apples fell to the ground. He wonders why they fell towards the earth and why they did not fly up into the sky.
According to the law which he later produced everything in the universe attracts everything else towards itself. The sun attracts the earth and the earth attracts the sun. The earth attracts the moon and the moon attracts the sun. Although the bigger object has the stronger attraction, all objects, in fact, have some attraction too but we do not notice the gravitational pull of a book because the pull of the earth is very much greater.
Why does the earth always move round the sun, and not fly off into cold space? The sun's gravitation gives the answer. The earth always tries to move away in a straight line, but the sun always pulls it back. So it continues on its journey round and round the sun.
The sun is one of the stars in the galaxy, in which there are about 100,000 million stars. It is not in the middle of the galaxy, but rather3 near one edge. These stars form a group, the shape of which is like the shape of a watch.
There are millions of galaxies in the universe and so there are thousands of millions of millions of suns. Many astronomers believe that some of these suns have planets as our sun does.
Gravitation is the force which holds all the atoms of a star together. It holds the sun together and it holds the atoms of the earth together. It holds us on the earth.
Einstein produced a new law of gravitation. Its main results are the same as the results of Newton’s law; but in very small and fine matters Einstein's law gives different results. One of these is that gravitation bends light a little; but according to Newton's law gravitation has very little effect on light. Einstein showed this fact by means of mathematics and not by experiment. And astronomers later proved by experiments that Einstein was right.
Notes
according to ‑ в соответствии с
in fact ‑ на самом деле, фактически
but rather ‑ а скорее