Friday, 5 June 2015

Hannah eats some sweets: easy

From The Daily Mail:

There are n sweets in a bag. Six of the sweets are orange. The rest of the sweets are yellow.

Hannah takes a 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 n^2-n-90=0

The answer, as so often, is in the question.

Rearrange "n^2-n-90=0" to "n2 - n = 90" and solve, n is obviously 10, then retrace your steps.

Probability of two oranges is: (6/n)x(5/n-1) = 30/n^2-n

We know that: "n^2-n" must be 90 (30 is one-third of 90)

As a check, substitute 10 for n in the first equation, (6/10)x(5/9) = 30/90 = one-third.

Is there anything more to it than that?


Random said...

The other way:
6/n multiplied by 5/n+1 = 1/3rd
30/n(n-1) equals 1/3
multiply by 3 to get 90/n(n+1) = 1
Multiply by n(n+1) to 90 = n(n+1)
N^2 - n = 90
N^2 - n - 90 = 0

buildingstoat said...

I think it is even easier than that,

Prob of 2 orange is:

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

30/n^2-n = 1/3

90/n^2-n = 1

n^2-n = 90

n^2-n -90 = 0


Mark In Mayenne said...

It also works for n= -9

Mark Wadsworth said...

R and BS that's exactly what I said

M you are a cad and a stinker - but well spotted

Random said...

I know, just working it out on the comment and sending it cos my brain is half asleep.

Sobers said...

Isn't the point about this problem that its not how easy (or hard) it is to solve (if I remember rightly I was solving quadratics by age 13), more that it threw into a tizzy all the GCSE students who have been spoon fed maths in such a way that they don't actually understand any principles at all, just have a 'When confronted with this equation do this, this and this to get the right answer' approach to maths? The fact they had to construct their own equation from basic principles rather than have it given to them on a plate was what was so shocking (to them). Hopefully this is evidence of Michael Gove's influence on exams and their rigorousness.

I met a maths teacher from a sink estate comp a few years ago, he freely admitted his entire 'success' as a teacher was based on the concept of identifying the natural D students, and putting all his effort into getting them a C, while leaving the rest to get on with it. He would provide the target pupils with sheets detailing exactly what to do to solve various types of problems that would be in the exams, and they would just learn the steps rote style. They had no idea of what they were doing, but it got them enough marks to get them over the C grade line, and thus made his results look good.

Mark Wadsworth said...

S, yes. It is all very worrying.

DBC Reed said...

Shows how poncified and precious school Maths is.If anything on the Arts side of the curriculum was so pointless and academic and boring and lacking beauty it would be crucified.Is it any wonder that the Sorbonne students in 2000 rebelled against their Economics syllabus which they described as "autistic" for being so fucked up by pure maths.Meanwhile 90% of MP's think that the State creates the money supply.

Mark Wadsworth said...

DBC, what's wrong with having a vague grasp of probabilities?

There's a bus every ten or fifteen minutes which costs £1 and might be full; or you can walk for half an hour but there's half a chance it will rain; or you can call a mini cab but there's quite a queue outside the mini cab office and they'll charge your group at least a tenner.

You have to make a decision. All of this is fuzzy maths but it is helpful.

Then we can focus in on Authoritarian bullshit like "Drinking wine increases the chance of breast cancer by 50% but reduces the risk of heart attacks by a quarter".

Belinda said...

The probability of any of the n sweets being orange is 6/n. That's true whether they're in the bag or outside the bag. The probability of any two of them both being orange is 36/(n x n). That probability can never be 1/3, its impossible. The examiners got it wrong and its no wonder the students were confused.

Mark Wadsworth said...

B, read the question properly:

"Hannah takes a sweet from the bag. She eats the sweet."

So the second time round there is one less* orange sweet and one less sweet overall.

The examiners made it too easy, if anything, because they gave you the answer.

* Or should that be "one fewer"?