Beware: Math(s) alert!

in reality, all of this has been a total load of old bollocks
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C
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Beware: Math(s) alert!

Postby C » 10 May 2021, 19:29

I know some of you like playing around with some mathematics.

My son who is doing his GCSE (assessments) at the moment (instead of the exams due to covid), wanted help with this question

I thought it was really nice:

Adam (yes, really!) has a bag with 6 lemon sherbets and n strawberry sweets.

Adam takes a sweet from the bag, replaces it, and takes another sweet from the bag.

The probability that Adam takes two lemon sweets is 1/9.

Write an equation to find the value of n, in the form nsquared + bn + c = 0

Nice.

Very nice






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Re: Beware: Math(s) alert!

Postby Rorschach » 11 May 2021, 07:26

C wrote:I know some of you like playing around with some mathematics.

My son who is doing his GCSE (assessments) at the moment (instead of the exams due to covid), wanted help with this question

I thought it was really nice:

Adam (yes, really!) has a bag with 6 lemon sherbets and n strawberry sweets.

Adam takes a sweet from the bag, replaces it, and takes another sweet from the bag.

The probability that Adam takes two lemon sweets is 1/9.

Write an equation to find the value of n, in the form nsquared + bn + c = 0

Nice.

Very nice.


God. I have no idea about these things. I'm really not sure what 'b' and 'c' are supposed to represent.

Anyway, while I work on that, can I check if I'm going in the right direction? Are there 12 strawberry sweets?

If I've got that right I'll try to reverse engineer it.
Bugger off.

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Re: Beware: Math(s) alert!

Postby Rorschach » 11 May 2021, 08:10

I've got it down to:

nsquared + 12n - 288 = 0

But I can't think how to take it any further.
Bugger off.

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Re: Beware: Math(s) alert!

Postby GoogaMooga » 11 May 2021, 10:27

Can't help you, math was my great bugbear in high school. I managed to get ZERO on the tests in calculus.
"When the desert comes, people will be sad; just as Cannery Row was sad when all the pilchards were caught and canned and eaten." - John Steinbeck

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Re: Beware: Math(s) alert!

Postby C » 11 May 2021, 11:47

Rorschach wrote:I've got it down to:

nsquared + 12n - 288 = 0

But I can't think how to take it any further.


That is the answer Tym, well done - it is in the form nsquared + bn + c = 0, which is what is required

Where a=1, b=12 and c= -288

The only reason for taking it further would be if the question required you to work out how many strawberry sweets there were. That is, find n

So,

You would need to find the roots of that quadratic and you would have to apply the formula as it doesn't obviously factorise

n = - b ± square root (bsquared - 4ac) all divided by 2a

n = -12 ± square root (144 + 1152) all divided by 2

n = (-12 ± 36)/2

n = 12 or - 24

So n = 12.

12 sweets are strawberry sweets

----------------------------------------------

If your mental mathematics is good you might notice that the quadratic does factorise

288 = 12 x 24 & 24-12 = 12

So

(n-12)(n+24) = 0

n = 12 n = -24

n = 12




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Re: Beware: Math(s) alert!

Postby C » 11 May 2021, 11:59

Rorschach wrote:
Anyway, while I work on that, can I check if I'm going in the right direction? Are there 12 strawberry sweets?

If I've got that right I'll try to reverse engineer it.


Correct.

The probability of a lemon sweet is 6/(6+n). [where (6+n) are the total number of sweets in the bag]

Replacing and taking another would be the same 6/(6+n)

So two taking two lemon sweets would be:

6/(6+n) X 6/(6+n) which equals 1/9

So 36/(36+ 12n + nsquared) = 1/9

Cross multiply

324 = 36+ 12n + nsquared

Simplifying:

nsquared + 12n - 288 = 0

Which is in the form nsquared + bn + c = 0 as required

Where a=1, b=12 and c= -288




.
Last edited by C on 11 May 2021, 15:18, edited 1 time in total.
Rorschach wrote:it [Tubular Bells] is indeed a very terrible thing. I had a nice Dusty Springfield song buzzing round my head before that bugger displaced it.

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Re: Beware: Math(s) alert!

Postby Rorschach » 11 May 2021, 12:46

C wrote:
Rorschach wrote:
Anyway, while I work on that, can I check if I'm going in the right direction? Are there 12 strawberry sweets?

If I've got that right I'll try to reverse engineer it.


Correct.

The probability of a lemon sweet is 6/(6+n). [where (6+n) are the total number of sweets in the bag]

Replacing and taking another would be the same 6/(6+n)

So two taking two lemon sweets would be:

6/(6+n) X 6/(6+n) which equals 1/9

So 36/(36+ 12n + nsquared) = 1/9

Cross multiply

3245(!!!) = 36+ 12n + nsquared

Simplifying:

nsquared + 12n - 288 = 0

Which is in the form nsquared + bn + c = 0 as required

Where a=1, b=12 and c= -288




.


More or less how I did it, but my original calculation to arrive at the number of strawberry sweets was a bit simpler that that!
I just thought that if two goes gave you a one in nine chance of getting two lemons, then one go must give you a one in three chance (the square root of nine). After that it's easy to to figure out that there are 12 strawberry sweets.

To get to the formula I did:

6/n+6 x 6/n+6 =1/9

(6 X 6)/(n+6) X (n+6) = 1/9

36/ nsquared + 12n + 36 = 1/9

324/ nsquared + 12n + 36 = 1

multiply both sides by nsquared + 12n + 36:

nsquared + 12n + 36 = 324

Subtract 324 from each side:

nsquared + 12n - 288 = 0
Last edited by Rorschach on 11 May 2021, 14:28, edited 1 time in total.
Bugger off.

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Re: Beware: Math(s) alert!

Postby Rorschach » 11 May 2021, 12:56

cock up...
Last edited by Rorschach on 11 May 2021, 14:28, edited 1 time in total.
Bugger off.

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Re: Beware: Math(s) alert!

Postby The Prof » 11 May 2021, 13:06

Glad I'm not doing GCSE's now.

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Re: Beware: Math(s) alert!

Postby der Freiherr » 11 May 2021, 13:14

C wrote:I know some of you like playing around with some mathematics.


Fucking sickos, every last one of you.
take5_d_shorterer wrote:If John Bonham simply didn't listen to enough Tommy Johnson or Blind Willie Mctell, that's his doing.

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Re: Beware: Math(s) alert!

Postby C » 11 May 2021, 15:19

Rorschach wrote:
C wrote:
Rorschach wrote:
Anyway, while I work on that, can I check if I'm going in the right direction? Are there 12 strawberry sweets?

If I've got that right I'll try to reverse engineer it.


Correct.

The probability of a lemon sweet is 6/(6+n). [where (6+n) are the total number of sweets in the bag]

Replacing and taking another would be the same 6/(6+n)

So two taking two lemon sweets would be:

6/(6+n) X 6/(6+n) which equals 1/9

So 36/(36+ 12n + nsquared) = 1/9

Cross multiply

324 = 36+ 12n + nsquared

Simplifying:

nsquared + 12n - 288 = 0

Which is in the form nsquared + bn + c = 0 as required

Where a=1, b=12 and c= -288




.


More or less how I did it, but my original calculation to arrive at the number of strawberry sweets was a bit simpler that that!
I just thought that if two goes gave you a one in nine chance of getting two lemons, then one go must give you a one in three chance (the square root of nine). After that it's easy to to figure out that there are 12 strawberry sweets.

To get to the formula I did:

6/n+6 x 6/n+6 =1/9

(6 X 6)/(n+6) X (n+6) = 1/9

36/ nsquared + 12n + 36 = 1/9

324/ nsquared + 12n + 36 = 1

multiply both sides by nsquared + 12n + 36:

nsquared + 12n + 36 = 324

Subtract 324 from each side:

nsquared + 12n - 288 = 0


Good lad and thanks for the typo!



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Re: Beware: Math(s) alert!

Postby Deebank » 11 May 2021, 15:20

The Prof wrote:Glad I'm not doing GCSE's now.



To be fair, no one is doing GCSEs now.
















(my daughter is having 'Assessments' though which pretty much amount to the same thing)
I've been talking about writing a book - 25 years of TEFL - for a few years now. I've got it in me.

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Re: Beware: Math(s) alert!

Postby C » 11 May 2021, 15:21

der Freiherr wrote:
C wrote:I know some of you like playing around with some mathematics.


Fucking sickos, every last one of you.


:lol:

The Prof wrote:Glad I'm not doing GCSE's now.


Yes. Agreed. And they talk about standards going down....





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Re: Beware: Math(s) alert!

Postby C » 11 May 2021, 15:26

Deebank wrote:
The Prof wrote:Glad I'm not doing GCSE's now.



To be fair, no one is doing GCSEs now.


Smart ass/arse comrade

I mentioned that in my opening post and the lad would have been aware! :lol:




Actually, I consider the assessments more stressful than the actual exams.

With the GCSE exams you get a timetable so you know what to focus/prioritise when.

With the assessments they are done in the lesson, in bits and pieces, over a longer period of time, with moving goal posts and all the teachers jockeying for position around priorities, additional work to justify preconceived grades with higher expectations of the students

Well, something like that comrade





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Rorschach wrote:it [Tubular Bells] is indeed a very terrible thing. I had a nice Dusty Springfield song buzzing round my head before that bugger displaced it.

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Re: Beware: Math(s) alert!

Postby Good Night Dallas, Texas » 11 May 2021, 16:21

There are 1000 independent lotteries. Each lottery has 1000 tickets and one drawn ticket wins each lottery.

If you buy a ticket for each lottery - 1000 tickets in total - what is the probability that you win AT LEAST one of the lotteries?

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Re: Beware: Math(s) alert!

Postby C » 11 May 2021, 17:03

Rorschach wrote:cock up...


:lol:




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Re: Beware: Math(s) alert!

Postby Deebank » 11 May 2021, 17:57

C wrote:
Deebank wrote:
The Prof wrote:Glad I'm not doing GCSE's now.



To be fair, no one is doing GCSEs now.


Smart ass/arse comrade

I mentioned that in my opening post and the lad would have been aware! :lol:




Actually, I consider the assessments more stressful than the actual exams.

With the GCSE exams you get a timetable so you know what to focus/prioritise when.

With the assessments they are done in the lesson, in bits and pieces, over a longer period of time, with moving goal posts and all the teachers jockeying for position around priorities, additional work to justify preconceived grades with higher expectations of the students

Well, something like that comrade





.


Yep, spot-on comrade. My daughter thought she was on easy street, "No exams!" the government said.
She should do OK though, her teachers thinks she's great.
I've been talking about writing a book - 25 years of TEFL - for a few years now. I've got it in me.

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Re: Beware: Math(s) alert!

Postby Rorschach » 11 May 2021, 21:30

Good Night Dallas, Texas wrote:There are 1000 independent lotteries. Each lottery has 1000 tickets and one drawn ticket wins each lottery.

If you buy a ticket for each lottery - 1000 tickets in total - what is the probability that you win AT LEAST one of the lotteries?



Aargh!
I can't remember how to calculate it. I know it isn't 1,000 in 1,000 but it has to be better than one in a thousand. I'm stuck there at the moment.
Bugger off.

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Re: Beware: Math(s) alert!

Postby Good Night Dallas, Texas » 11 May 2021, 22:06

Rorschach wrote:
Good Night Dallas, Texas wrote:There are 1000 independent lotteries. Each lottery has 1000 tickets and one drawn ticket wins each lottery.

If you buy a ticket for each lottery - 1000 tickets in total - what is the probability that you win AT LEAST one of the lotteries?



Aargh!
I can't remember how to calculate it. I know it isn't 1,000 in 1,000 but it has to be better than one in a thousand. I'm stuck there at the moment.


Calculate the probability that you don't win any of the 1000 lotteries.

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Re: Beware: Math(s) alert!

Postby The Prof » 12 May 2021, 10:05

Each lottery is a 1/1000 to one chance. If you do 999 lotteries and lose each time, when you get to the 1000th one, it's still 1/1000.

You should stand a greater chance of winning on at least one of them, so is it 1/901? - or something like that?