GCSE Maths question

fastwunz

fastwunz

fastwunz

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Ok - am I missing something here? Apparently loads of GCSE students are complaining about this question:

There are 'n' sweets in a bag.

6 of the sweets are orange.
The rest are yellow.

Hannah takes one sweet at random.
She eats the sweet.

She takes another sweet at random.
She eats the sweet.

The probability that Hannah eats two orange sweets is 1/3

a) Show that n(squared) - n - 90 = 0

Erm surely this is REALLY easy? - actually no............... no it isnt.
 
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There are six orange sweets and n sweets overall. If she takes one, there is a 6/n chance of getting and orange sweet. When she takes one, there is one less orange sweet and one less sweet overall.
If she took another orange sweet, the probability would be (6-1)/(n-1)=5/n-1. Now, you have to find the probability if she gets two orange sweets so you simply times the two fractions: 6/n * 5/n-1 = 30/n^2-n.
It tells us the probability of two orange sweets is 1/3 which means 1/3=30/n^2-n.
We need to make the denominators the same so simply times 1/3 by 30/30 which would equal 30/90. if 30/90 = 30/n^2-n, then n^2-n=90. if n^2-n=90 then n^2-n-90 will equal zero.
 
Its dead easy. I saw this about ten mins ago and solved it quickly enough.

Also saying the answer is n=10 when the question asks you to show how the equation is formed is pointless.

But showing how the equation is formed is easy.
 
it is straightforward for adults, at GCSE it is probably set in one of the higher level papers.... long time since I did GCSEs but I remember having to sit papers 8,9 and 10... with paper 10 required for an A* I would guess the question is in one of those.

Interestingly though as 'easy' as it is people are seemingly confused by it - there was a telegraph article today about it where the journalist got the question wrong and informed the readers that the answer was n = 10

lots of people in the comments similarly misinterpreted the question

the question asks you to prove n2 - n - 90 = 0

the answer is in Xordium's post above

you are given that there are 6 orange sweets... and that the probability of picking two at random is 1/3

you then deduce that the probability of picking the first one is 6/n and the probability of picking the second is 5/(n-1)... you realise that these are independent events and so 6/n * 5/(n-1) = 1/3

you then rearrange as per Xordium's post
 
factorise (n-10)(n+9)=0

n=10 or n=-9 satisfies the equation, and it can't be negative so n=10

edit: just realised it's not about solving the equation at all, Tom0 /thread
 
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fastwunz said:
nope - head hurts.
Click to expand...

n does =10, just not what it's asking for. It's asking to derive the equation.

Like if I said "show that 5+6=3+2x is equivalent to 8=2x". You rearrange it, next question would be "what is x" (or in this case n).

(Very basic example I know :D)
 
i'd have worked backwards, factorised the equation, and checked if the values matched the possible number of sweets.

like many exams, this will be the question worded to try and trip the student up and the lesson to be learnt isn't so much the maths [assuming said maths was taught to any level of competency] as the way to go about solving problems.
 
Yellow = 10
If 6 orange and 1/3 chance of eating orange then 2/3 chance of eating yellow, so that's 6 * 5/3.

6 * 5/3 = 10

But as said you need to know the probability equations.
 
jsmoke said:
Yellow = 10
If 6 orange and 1/3 chance of eating orange then 2/3 chance of eating yellow, so that's 6 * 5/3.

6 * 5/3 = 10

But as said you need to know the probability equations.
Click to expand...

Er what. n = 10 = Total sweets. 6 Orange sweets therefore must be 4 yellow.

Also its 1/3 probability to eat two oranges.
 
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