Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena.The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. If an individual coin toss or the roll of dice is considered to be a random event, then if repeated many times the sequence of random events will exhibit certain patterns, which can be studied and predicted. Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem. As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.
Maths is essential
I think mathematics is a very important subject. We need to know our numbers no matter what career we choose.
Maths is indispensable, whether you are buying, selling or promoting products. Countries around the world depend on trade to improve people's livelihoods. So where would we be without maths? Even street-side vendors have a basic knowledge of maths. Otherwise, they can't do business.
So, you students, remember that maths can have a direct impact on your income. You may not like maths, but you can't ignore it.
Love your parents, and they'll love you
Sadness seems to be everywhere these days. Some adults are so depressed they will do almost anything to escape their problems. For example, there have been several family tragedies in Tin Shui Wai, the 'city of sadness'.
Many local youngsters are unhappy, too. Some of them take drugs to ease their study pressure, while a number of teenage girls are involved in compensated dating.
More and more young girls are selling their bodies for money and this is very bad. Most of these girls are jobless, while some are still at school.
It's a lack of love from friends and family that leads to such behaviour.
Our parents also face many obstacles. They have to work hard to make ends meet and are often stressed after their tiring days at the office.
Maybe we can give them a kiss or hug and cheer them up. We could also prepare some gifts for them. If we love them, they will love us.
We are lucky to be living in a prosperous city like Hong Kong. We should treasure our opportunities and express our love to the people around us.
Kammy Lo Yuen-shan, Tsuen Wan Public Ho Chuen Yiu Memorial College
Need for a better drug-testing scheme
I want to express my views about the proposed drug-testing scheme in local schools. I believe the real issue here is one of privacy, not whether a student has the right to refuse a drug test.
Teenagers should speak out about this government proposal. It doesn't matter whether they are taking drugs or not. Students have the right to privacy.
I also do not think it is right that officials only need parental consent to take urine samples from under-18s. Minors should also have a say in whether they undergo drug tests.
I agree that teenage drug abuse is a serious problem in Hong Kong. But the government should come up with a better proposal. Officials should put in place privacy measures and ensure the results are confidential.
Cheng Chi-yan, Kit Sam Lam Bing Yim Secondary School
About time ...
What can you do in a minute? You can eat a sweet, have a short discussion or save someone's life.
For example, firemen who arrived at a blaze a minute earlier could have saved more lives.
A minute a day means 365 minutes over 12 months. If we use this time to help others, our lives will be much more meaningful.
Meek Yang, SKH Bishop Mok Sau Tseng Secondary School
Don't give up, try harder
Life is not only about getting high marks. The more important thing is to not to give up, even if you get poor grades.
We all have different abilities, but we should try our best in whatever we do. There may be cleverer students, but you can reach the same standard through hard work. Besides, you may be better than others at playing the piano or violin, singing, dancing or basketball.
There is more to life than exam success.