Are you smarter than a sixteen year old?

[Tal]

Hannah has 6 orange sweets and some yellow ones.

Overall, she has n sweets.

The probability of her taking two orange sweets is 1/3

Prove that n²-n-90=0


(Taken from this year's GCSE Maths paper)

[mulhuzz]

Started a more 'fun' proof using binomial coefficient and then went 'nah, why don't I just do it the easy way'

6/n x 5/n-1 = 1/3.

[Tal]

I can't get over the furore this has caused, notwithstanding it's a poorly worded question.

[mulhuzz]

I can't get over the furore this has caused, notwithstanding it's a poorly worded question.

How is it poorly worded?

Seems to be some pretty poor furore!

[Tal]

I can't get over the furore this has caused, notwithstanding it's a poorly worded question.

How is it poorly worded?

Seems to be some pretty poor furore!

The link between the third and fourth sentences is not easy to follow. What does that equation have to do with 1/3?

Not everybody can equate maths to real life. Test people's ability to do the maths, rather than their ability to understand the question.

[DungBeetle]

I don't understand why the question is bad?  Seems okay to me - construct a formula and simplify it to get to the proof?

[GreekStein]

I can't get over the furore this has caused, notwithstanding it's a poorly worded question.

How is it poorly worded?

Seems to be some pretty poor furore!

The link between the third and fourth sentences is not easy to follow. What does that equation have to do with 1/3?

Not everybody can equate maths to real life. Test people's ability to do the maths, rather than their ability to understand the question.

But all maths is related to some kind of question, no? If someone can solve that formula but not understand the question then....

[Jon MW]

I don't understand why the question is bad?  Seems okay to me - construct a formula and simplify it to get to the proof?

I think the complaint wasn't that it was difficult per se - but that it wasn't consistent with the difficulty level they were being taught to and had appeared in previous year's exam papers.

[Tal]

I can't get over the furore this has caused, notwithstanding it's a poorly worded question.

How is it poorly worded?

Seems to be some pretty poor furore!

The link between the third and fourth sentences is not easy to follow. What does that equation have to do with 1/3?

Not everybody can equate maths to real life. Test people's ability to do the maths, rather than their ability to understand the question.

But all maths is related to some kind of question, no? If someone can solve that formula but not understand the question then....

Of course, but my reading of the feedback on the internet and in the news is that people struggled to understand what the question was asking of them. The maths bit is fairly straightforward (if you've been studying algebra). Here's an alternative last sentence...

Hannah has 6 orange sweets and some yellow ones.

Overall, she has n sweets.

The probability of her taking two orange sweets is 1/3.

Show that the probability of her picking two orange sweets in her two next selections can be rewritten as n²-n-90=0

[doubleup]

not sure that helps Tal

ironically I couldn't have answered the question when I was 16 but can have a decent go now

(6*5/2)/(n*(n-1)/2)=1/3

45/(n*(n-1)/2)=1

45=(n*(n-1)/2)

90=n*(n-1)

0 = (n*(n-1))-90

0 = n2-n-90

(I think)


edit bloody brackets

[RED-DOG]

I don't like orange sweets.

[Tal]

I don't like orange sweets.

Good job Hannah does, then.

[Doobs]

I can't get over the furore this has caused, notwithstanding it's a poorly worded question.

How is it poorly worded?

Seems to be some pretty poor furore!

The link between the third and fourth sentences is not easy to follow. What does that equation have to do with 1/3?

Not everybody can equate maths to real life. Test people's ability to do the maths, rather than their ability to understand the question.

But all maths is related to some kind of question, no? If someone can solve that formula but not understand the question then....

Of course, but my reading of the feedback on the internet and in the news is that people struggled to understand what the question was asking of them. The maths bit is fairly straightforward (if you've been studying algebra). Here's an alternative last sentence...

Hannah has 6 orange sweets and some yellow ones.

Overall, she has n sweets.

The probability of her taking two orange sweets is 1/3.

Show that the probability of her picking two orange sweets in her two next selections can be rewritten as n²-n-90=0

I think people are always going to have barriers when asked to prove something now.  

It was definitely one of my pet hates and I did a maths degree.  Proofs are a doddle if you remember them, but not so much when you have to do them from scratch.  

Getting asked to prove something from scratch is just going to appear really hard to a lot of children.  It is getting over that psychological barrier that helps you see the question for what it is something that is not something that is easy to do under the stressful conditions of a significant exam.  I expect it would be something that I'd have found difficult at 16.  I am sure it was quite a bit after that where I learned to just move on to the next question if something was too difficult.  

FWIW It doesn't even look that easy when I saw the question for what it was.

[AdamM]

Does it drive you mad when those irritating like-farming memes go round facebook and the vast majority of people would answer a question like 2 + 2 x 0 + 2 as 2 rather than 4?

That must mean that the majority of people would also completely fail a question like the one in the OP

[Cf]

The probability of picking the two sweets can be expressed as:

6/n * 5/(n-1) = 1/3

Numerator 6 * 5 = 30 so the denominator must be 90

n(n-1) = 90

n(n-1) - 90 = 0

n^2 - n - 90 = 0


Really don't see what the fuss is about. Question is worded absolutely fine.

If people think that's bad they're going to be in for a shock in a couple of years time. This question is easy compared with what is planned to come.

(Edit - Simplified the simplifying)