A math question has been stumping thousands of British students

Many people have the notion that UK British GCSE is very easy, but there seems to be a very tough Probability question that has appeared!

Here’s the question on the test, which was set by the British education and examination board Edexcel

There are n sweets in a bag. Six of the sweets are orange. The rest of the sweets are yellow. Hannah takes a random sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag. She eats the sweet. The probability that Hannah eats two orange sweets is 1/3. Show that n²-n-90=0.

Source: http://mashable.com/2015/06/05/math-exam-gcse-question/

This is really one tough question for 15, 16 year old kids.

Do try it out, and if you are stuck you can check out the solution by Professor Ian Dryden, the head of mathematical sciences at the University of Nottingham, at the link above.

Probability Demystified 2/E

Check out this book to get enlightened on the mysterious topic of probability.

Coursera Probability Course and Recommended Probability Book

Just completed the Coursera Probability Course by UPenn (University of Pennsylvania), lectured by Professor Santosh S. Venkatesh who is the author of the highly recommended book: The Theory of Probability: Explorations and Applications.

Coursera Review

The course isn’t very hard, it is very suitable for undergraduates and even high school students should be able to understand majority of the content. It actually overlaps with the A level syllabus in Singapore, and hence I would say that a 17-18 year old student would be able to grasp most of the concepts in this course.

The lecturer is very good at words, and his lectures are full of imagery and vivid descriptions. The homework is a little tricky, and hence would require some thought, even though the concepts tested are elementary (elementary in the sense that it doesn’t require calculus).

A sample of a tricky question is the “Six Saucer Question”: Six cups and saucers come in pairs: there are two cups and saucers that are red, white, and blue. If the cups are placed randomly onto the saucers (one each), find the probability that no cup is upon a saucer of the same color.

It is very tricky and to get it correct on the first try is a major accomplishment.

Overall, this Coursera Course is highly recommended, and students should try to take it the next time it comes out!

Xinmin Secondary 2010 Prelim Paper I Q24 Solution (Challenging/Difficult Probability O Level Question)

Just to reblog this earlier post on a really challenging Probability O Level Question.

Also, do check out my other related posts on Probability:

Probability is becoming a really important branch of mathematics. One of the most famous Singaporean mathematicians is Professor Louis Chen Hsiao Yun who has a theorem named after him! (Stein-Chen method of Poisson approximation) Professor Chen researches on Probability.

To begin your journey in Probabilty, Introduction to Probability, 2nd Edition is a good book to start learning from. An intuitive, yet precise introduction to probability theory, stochastic processes, and probabilistic models used in science, engineering, economics, and related fields. You may also wish to refer to our comprehensive list of Recommended Undergraduate Books.

(One of the best books to begin your journey in studying the mysterious topic of Probability)

 

Singapore Maths Tuition

A bag A contains 9 black balls, 6 white balls and 3 red balls. A bag B contains 6 black balls, 2 white balls and 4 green balls. Ali takes out 1 ball from each bag randomly. When Ali takes out 1 ball from one bag, he will put it into the other bag and then takes out one ball from that bag. Find the probability that

(a) the ball is black from bag A, followed by white from bag B,
(b) both the balls are white in colour,
(c) the ball is black or white from bag B, followed by red from bag A,
(d) both the balls are of different colours,
(e) both the balls are not black or white in colours.

probability maths tuition

Solution:

(a) $latex displaystylefrac{9}{18}timesfrac{2}{13}=frac{1}{13}$

(b) Probability of white ball from bag A, followed by white ball from bag B=$latex displaystyle=frac{1}{2}timesfrac{6}{18}timesfrac{3}{13}=frac{1}{26}$

Probability of white from B, followed…

View original post 105 more words

Exciting New Math Course at Probability, and Book by Eccentric Mathematician

Recently, I just finished my Coursera course on Cryptography, and I have started a brand new course on Probability. This is a rather introductory course on Probability, probably at the junior undergraduate level. However, looking at the course syllabus, later on in the course some deeper aspects of probability will be taught.

Welcome message from the Probability team:

Thank you for signing up for Probability!  This is a beguiling subject with a fascinating historical tradition and vibrant modern applications.  We are delighted that you are joining us in this journey of exploration.  And you are entitled to bask in the warm light of the realisation that you are one of the pioneers in a novel form of online learning!

Class has already begun, so please join us.  We are looking forward immensely to our journey together!

Best wishes,
The Probability Course Team

The course is based on the book by Professor Venkatesh: The Theory of Probability: Explorations and Applications. Rated 5/5 on Amazon, this book is a good read, and covers many aspects of probability theory.

Another new Math book on the international scene is Birth of a Theorem: A Mathematical Adventure by the eccentric French Mathematician Cédric Villani who received the Fields’ Medal in 2010. It contains the story of his life,  his favorite songs, his love of manga, and the imaginative stories he tells his children.

Cédric Villani

 

 

Finding E Maths or A Maths Difficult?

Are you finding Elementary Maths (E Maths) or Additional Maths (A Maths) Difficult?

Do not be discouraged if you find E Maths or A Maths difficult. The main reason why you are finding it to be difficult is that it is new. You have not gotten enough exposure to the type of questions asked. It is like learning to ride a bicycle, at the start it is difficult and you may even fall down. But after you have mastered riding the bicycle, you will be able to ride as fast as you wish. You need to get over the initial difficulty of learning in order to master the art of riding the bicycle.

At our Group Tuition at Bishan, we constantly practice actual exam questions, be it on Trigonometry, Differentiation or Integration (A Maths), or Vectors, Matrices and Probability (E Maths). We learn different methods to check and do the questions. You will find out, at last, that once you master the art of solving O Level questions, all the O Level questions are just repackaging the same questions in different forms. Once you know how to do one question, you will know how to do all similar questions. Expanding your repertoire of questions you know will enable you to get that coveted “A”. Constant practice, as opposed to cramming one month before the O Levels, is absolutely necessary to avoid panic and to consolidate our Mathematical memory.

Some Math formulas like the quotient rule, \displaystyle\frac{d}{dx}(\frac{u}{v})=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}, you will automatically memorize it once you have done enough practice.

In the end, you may even find that E Maths or A Maths is easy!


Motivational Story to motivate you

(Source: http://www.indianchild.com/inspiring_stories.htm)

THE OBSTACLE IN OUR PATH
In ancient times, a king had a boulder placed on a roadway. Then he hid himself and watched to see if anyone would remove the huge rock. Some of the king’s wealthiest merchants and courtiers came by and simply walked around it.

Many loudly blamed the king for not keeping the roads clear, but none did anything about getting the big stone out of the way. Then a peasant came along carrying a load of vegetables. On approaching the boulder, the peasant laid down his burden and tried to move the stone to the side of the road. After much pushing and straining, he finally succeeded. As the peasant picked up his load of vegetables, he noticed a purse lying in the road where the boulder had been. The purse contained many gold coins and a note from the king indicating that the gold was for the person who removed the boulder from the roadway. The peasant learned what many others never understand.

Every obstacle presents an opportunity to improve one’s condition.


Chinese Version

石头的故事

从前有一个国王,他故意派人搬来一块大石头放在道路中间。然后这个国王躲在旁边静静地观察,想知道是否会有人过来把这块大石头搬走。有几个富有的商人经过这块石头,只是直接绕过它。之后又来了几个人,他们只是埋怨国王居然没有找人来清理道路,然后仍然是绕过这块巨石走掉了。又过了一会,一个农夫经过这里,他身上背着沉甸甸的蔬菜。走到巨石的前面,把身上背的蔬菜放下,然后试着去把这块巨大的石头移到道路的旁边。农夫竭尽全力去推那块巨石,终于成功得把石头推到道路的一侧。农夫背起蔬菜准备继续赶路,却发现石头原来所在的地方下面有一个袋子。农夫好奇得打开袋子,里面有许多金币还有一个纸条。纸条是国王留下的,原来金币是用来奖励移走石头的人。
这个小故事讲述了一个简单的道理:困境也有可能是机会。遇到困难的时候,有些人会像商人那样,直接选择放弃。有些人会像那几个埋怨者,只会抱怨却不想着付出行动来改变现状。很少人会像故事中的农夫那样选择迎难而上。然而,最终收获最多的往往就是这部分迎难而上的人。
平常生活中和工作中也是这样,遇到问题,首先要不抛弃不放弃,积极寻求解决方法。无休止的抱怨只会白白错失机会,抱怨多了,好运气也会绕道而行。在困境中寻找机会方法,在挫折中吸取经验教训,那么就会很容易走出困境了,说不定还会有意外的收获哦!

Probability Formula

Formulae for Probability

Works for All Cases:

  1. P(A∪B)=P(A)+P(B)-P(A∩B)

  2. P(A|B)=\displaystyle\frac{P(A\cap B)}{P(B)}

  3. P(A’)=1-P(A)


For Mutually Exclusive Events Only:

  1. P(A∩B)=0

Mutually Exclusive
Mutually Exclusive


For Independent Events Only:

  1. P(A∩B)=P(A) P(B)

  2. P(A|B)=P(A)

  3. P(B|A)=P(B)

  4. P(A’∩B)=P(A’) P(B)

  5. P(A∩B’)=P(A) P(B’)

  6. P(A’∩B’)=P(A’) P(B’)