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.
Mathtuition88 
An interesting question combinaing Probability and Algebra !
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The British Math system which Singaporeans inherit at Sec school is applied and non-abstract thinking. The fact that it uses abstract ‘n’ (instead of concrete number, say, 10), the students’ brain cannot visualize ‘n’ sweets.
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The French students, on the opposite, abstract since Sec 3, but not very applied.
It is good to have both applied and abstract Math from Sec3/4.
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The French students, on the opposite, abstract since Sec 3 (eg. Group, epsilon-delta Calculus, vector space…), but not very applied.
It is good to have the best of both worlds: applied and abstract Math from Sec3 /4.
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Here’s my proof:
Let n be the total number of sweets in the bag. The probability that the 1st sweet is orange is 6/n. Assuming that the 1st sweet was orange, the probability that the 2nd sweet is also orange would be 5/(n-1). Since the probability that Hannah eats 2 orange sweets is 1/3, we have the probability that both sweets are orange is 6/n x 5/(n-1) = 1/3.
Multiplying the left hand side together we get 30/(n^2 – n) = 1/3.
Cross multiplying we get 90 = (n^2 – n) which is equivalent to n^2 – n – 90 = 0.
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Nice and concise! Thanks for posting your solution. 🙂
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The problem’s not hard exactly, but swinging from a probability question to a manipulate-the-algebraic-expression problem partway through is bizarre. Who does that?
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Yeah good point, thanks for your comment! The UK GCSE is notorious for being too easy, I guess they are trying to reverse their reputation!
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