Another Maths Question For You

[PhilippineSaint]

Are we talking a priori or a posteori? Sticking with the door is 33%. The alternative must be 66%

 

It's called the Monty Hall problem:

 

http://en.wikipedia.org/wiki/Monty_Hall_problem

 

Originally it would have been priori but as its now posteori I could come along to your way of thinking but with certain reservations depending on if you had a good or bad host.

[Bearsy]

It's balls! I ain't having it! Way I see it is I'm being asked to guess again and it don't make a fat bit of difference whether there was originally 3 doors or a billion doors. There's only two doors now and Tokyos is behind one of them! I could flip a coin!

 

I'm getting a bit fed up with all you weird beards with your calculators and brown leather sandals!

[Ken Tone]

I left school with a Grade A O'Level Maths in 1978:blush:but don't recall anything other than left to right, brackets first. Would I have been taught "wrong" or just not progressed onto that level of maths (after all infants are taught correctly in basic addition etc but wouldn't have a clue about square roots etc) . If Bidmas is now taught in schools no wonder I was no use to my kids helping with their homework

 

 

3+4x5 = 23 Absolutely no doubt whatsoever -- basic rules of arithmetic. If you think it is 35, you were indeed taught 'wrong' and should sue the school!

 

 

You may not have been taught the mnemonic BODMAS, or one of its variants , but you should have been told that multiplication and division (equally) take precedence over addition and subtraction (equally)...and that brackets , then any form of power, take precedence over the others.

 

It is because, as you say, little kids do not understand powers (including fractional powers such as square roots) that some primary schools used to teach BODMAS ,with the 'O' as 'of' , as a stop gap to be replaced by 'order' later, but *I think that has gone out of fashion.

[PhilippineSaint]

It's balls! I ain't having it! Way I see it is I'm being asked to guess again and it don't make a fat bit of difference whether there was originally 3 doors or a billion doors. There's only two doors now and Tokyos is behind one of them! I could flip a coin!

 

I'm getting a bit fed up with all you weird beards with your calculators and brown leather sandals!

 

And the chances of it coming down on its edge so you lose Tokyo to me with you not being able to open either of the remaining doors??

[Bearsy]

I don't even get my goat? Bummer

[saintbletch]

Are we talking a priori or a posteori? Sticking with the door is 33%. The alternative must be 66%

 

Sorry Bear your beeatch is gone. Sorry PhilippineSaint, you can tell the lady boy hospital to put the darning needle away.

 

Tokyo-Saint is heading to Whitey Grandad's place.

 

Quite counter-intuitively, you increase your chances of winning if you always change your original selection once given the new information. It's 2/3 if you change.

 

Most people assume a 1/3 chance of finding the car with Tokyo-Saint in the boot. Which is true when you have no additional knowledge.

 

When we find that we know one of the incorrect doors, most people assume that the odds are the same. Or that they've now become 50/50 (one door or the other) and therefore there is no benefit in changing your mind.

 

Think of it this way. By taking a strategy of changing your mind, you only lose if you originally guessed the correct door (1/3). So you will win in 2/3 occasions.

[View From The Top]

The 'goat' problem is a standard statistics/probability brain teaser. I remember one of my Maths lecturers at uni giving us this in the 1970's, albeit expressed as a 'find the lady' gambling game, but the same principle.

 

The logic is .....

 

You should obviously change your mind if your first choice was wrong

 

When you made that choice there was a 1/3 chance you were right and a 2/3 chance you were wrong.

 

Therefore you were more likely to have been wrong and should change your choice.

 

One of my student teachers used it as a demonstration for other teachers using paper cups & jelly babies.

 

Worked brilliantly.

[PhilippineSaint]

Sorry Bear your beeatch is gone. Sorry PhilippineSaint, you can tell the lady boy hospital to put the darning needle away.

 

Tokyo-Saint is heading to Whitey Grandad's place.

 

Quite counter-intuitively, you increase your chances of winning if you always change your original selection once given the new information. It's 2/3 if you change.

 

Most people assume a 1/3 chance of finding the car with Tokyo-Saint in the boot. Which is true when you have no additional knowledge.

 

When we find that we know one of the incorrect doors, most people assume that the odds are the same. Or that they've now become 50/50 (one door or the other) and therefore there is no benefit in changing your mind.

 

Think of it this way. By taking a strategy of changing your mind, you only lose if you originally guessed the correct door (1/3). So you will win in 2/3 occasions.

 

Does this mean that Whitey Grandad can now change Tokyo's avatar ??

[Ken Tone]

One of my student teachers used it as a demonstration for other teachers using paper cups & jelly babies.

 

Worked brilliantly.

 

You mean they did it enough times to show an actual difference in success rates depending on whether you change or not? I've never seen that done. Always assumed it would take hundreds of attempts to get a clear pattern. Restores one's faith in theory!

[Ken Tone]

I don't even get my goat? Bummer

 

 

I shall restrict myself to saying that your personal predelictions for 'entertainment', are entirely your own business Bearsy. I'm just relieved for the goat's sense of self worth and physical comfort

[Deano6]

May have been on here before, it was being discussed on radio yesterday and they said it was doing rounds on the internet.

 

6-1*0+2/2 = ?

 

I got it hopelessly wrong:blush:

 

It was called BODMAS in my day. Calculators vary in their priority sequencing. HP used to use reverse Polish which confused some people.

 

1 to the power 0 is 1, so the answer is 6-1+1, which is 1.

 

Worst maths ever??

 

It's balls! I ain't having it! Way I see it is I'm being asked to guess again and it don't make a fat bit of difference whether there was originally 3 doors or a billion doors. There's only two doors now and Tokyos is behind one of them! I could flip a coin!

 

I'm getting a bit fed up with all you weird beards with your calculators and brown leather sandals!

 

Funnily enough Poppa Bear, the way our lecturer at Uni spelled it out was to imagine the game is a billion doors. You pick one, the host then opens all but one of the remaining doors (1 billion minus 2, whatever that is) which he knows don't contain Tokyos. What do you do now - stick with your 1 in a billion shot, or take the other side of that bet ("1 billion minus 1"-in-a-billion, whatever that is)? Remember it's Tokyos bum on the line here!

[saintbletch]

You mean they did it enough times to show an actual difference in success rates depending on whether you change or not? I've never seen that done. Always assumed it would take hundreds of attempts to get a clear pattern. Restores one's faith in theory!

 

It looks like you start to see the pattern pretty quickly.

 

Here's a Monte Carlo simulation over 30 events.

 

http://en.wikipedia.org/wiki/File:Monty_problem_monte_carlo.svg

[Big Bad Bob]

3+4x5 = 23 Absolutely no doubt whatsoever -- basic rules of arithmetic. If you think it is 35, you were indeed taught 'wrong' and should sue the school!

 

Absolute ******, I got an A at 'O' level maths and a B at 'A' level maths and I was never taught about order and precedence in maths, it was always left to right (unless of course parentheses are employed)!

 

If you wanted something done before something else you'd put parentheses around it, therefore you would have been better writing 3+(4*5).

 

It's only since "getting into" computing that I learnt about the logical order of things in maths statements and about programming using parentheses.

 

Maybe that has now filtered down to how they teach things at school....

[Wes Tender]

As there is only one car and you can only choose 1 door it reverts to 50% when the first goat is removed from the 3rd door. and you swap doors.

 

But why do you say that it is the first goat behind the third door? As the other goat must be behind either in the first or second doors, the one behind the third door has to be the second goat.

[saintbletch]

Does this mean that Whitey Grandad can now change Tokyo's avatar ??

 

I'm not a lawyer PhilippineSaint but I think it means that Tokyo-Saint basically now belongs to Whitey Grandad. In the same way that he used to belong to Bearsy. So, yep new avatar for Tokyo-Saint I think.

 

All because the Bear left him gimped-up in the boot of his car while he was on the game show.

 

At least he didn't go home empty handed.

 

[Wes Tender]

Absolute ******, I got an A at 'O' level maths and a B at 'A' level maths and I was never taught about order and precedence in maths, it was always left to right (unless of course parentheses are employed)!

 

If you wanted something done before something else you'd put parentheses around it, therefore you would have been better writing 3+(4*5).

 

It's only since "getting into" computing that I learnt about the logical order of things in maths statements and about programming using parentheses.

 

Maybe that has now filtered down to how they teach things at school....

Ditto. Without the brackets, you would do it in the order it's written, at least for the sake of those of us of more advanced years. I'm entirely happy with algebra, but why would some idiot leave off the brackets, unless it was deliberately to confuse everybody?

[View From The Top]

You mean they did it enough times to show an actual difference in success rates depending on whether you change or not? I've never seen that done. Always assumed it would take hundreds of attempts to get a clear pattern. Restores one's faith in theory!

 

Two rows of tables, each with about 50 lines of 3. Worked a treat.

[PhilippineSaint]

I'm not a lawyer PhilippineSaint but I think it means that Tokyo-Saint basically now belongs to Whitey Grandad. In the same way that he used to belong to Bearsy. So, yep new avatar for Tokyo-Saint I think.

 

All because the Bear left him gimped-up in the boot of his car while he was on the game show.

 

At least he didn't go home empty handed.

 

 

I dont want a used goat of Bearsy,

 

Although it should be nice and tender and will do for Sunday lunch

[Ken Tone]

Absolute ******, I got an A at 'O' level maths and a B at 'A' level maths and I was never taught about order and precedence in maths, it was always left to right (unless of course parentheses are employed)!

 

If you wanted something done before something else you'd put parentheses around it, therefore you would have been better writing 3+(4*5).

 

It's only since "getting into" computing that I learnt about the logical order of things in maths statements and about programming using parentheses.

 

Maybe that has now filtered down to how they teach things at school....

 

Sorry mate but you are wrong. Has been taught in schools since time immemorial. How the hell do you think you sorted out algrebraic expressions like 3y^2 as opposed to (3y) ^2 if you didn't use true algebraic logic, which is what BODMAs represents?

 

Oh and I see your A level and raise you with my Maths degree, from 1974, and my first job , teaching Maths in the 70's, including of course BODMAS

[Frank's cousin]

Who's nicke dteh brackets - would always have been tought to include them in these sorts of sums, then it becomes easy...

[Wes Tender]

But getting back to the goats and the car behind those doors, are we all in agreement that the goat behind the third door has to be the second goat, because the first goat is behind either the first or the second door?

[Viking Warrior]

so what is the answer 7 or 1

 

I hated algebra anyway

[PhilippineSaint]

But getting back to the goats and the car behind those doors, are we all in agreement that the goat behind the third door has to be the second goat, because the first goat is behind either the first or the second door?

 

I cant agree to that as that goat may have been swapped with the goat behind the first or second door so may have been the first first goat and the first goat was really the old goat driving the car or is that Tokyo?

[Wes Tender]

so what is the answer 7 or 1

 

I hated algebra anyway

 

It depends on your age, VW. If you're over 50, the answer is 1. If you're younger, the answer is 7.

[Whitey Grandad]

Worst maths ever??

 

Oops. I've had bigger bloomers than that. Thank you for pointing it out, I knew someone would ;-)

 

I blame my IPAD. And not checking my results, but at least I showed my working so I must get some points for that.

[Big Bad Bob]

Sorry mate but you are wrong. Has been taught in schools since time immemorial. How the hell do you think you sorted out algrebraic expressions like 3y^2 as opposed to (3y) ^2 if you didn't use true algebraic logic, which is what BODMAs represents?

 

Oh and I see your A level and raise you with my Maths degree, from 1974, and my first job , teaching Maths in the 70's, including of course BODMAS

 

Jeez, I wasn't bragging I was just pointing out that I was never taught it! I have a degree too (Physic with Modern Computing) and I don't even remember any precedence rules in the maths I was taught doing that....

 

Funnily enough I was talking to a guy at work who is 23 and he knew about BODMAS.

 

And funnily enough your y^2 got me thinking about what we accept, cos if I see 3y^2 I take it as 3 * (y^2) not (3 * y)^2.

 

Reading the wikipedia article on it the bit that stick out for me is :-

 

Since the introduction of modern algebraic notation, multiplication has taken precedence over addition.[1] Thus 3 + 4 × 5 = 4 × 5 + 3 = 23. When exponents were first introduced in the 16th and 17th centuries, exponents took precedence over both addition and multiplication and could be placed only as a superscript to the right of their base. Thus 3 + 52 = 28 and 3 × 52 = 75. To change the order of operations, originally a vinculum (an overline or underline) was used. Today, parentheses or brackets are used to explicitly denote precedence by grouping parts of an expression that should be evaluated first. Thus, to force addition to precede multiplication, we write (2 + 3) × 4 = 20, and to force addition to precede exponentiation, we write (3 + 5)2 = 64.

 

BUT we're getting away here, because we're talking about algebraic notation, not a simple sum as first mooted in the thread, ie the diff between A+BC or A+B*C

 

So, for mine, the answer is 1, so there

 

Oh and try 1+2*3 using the calculator in Windows (if you use windows) in basic and scientific mode, former gives you 9, latter gives you 7. Not confusing in the slightest is it........

[Whitey Grandad]

What's a calculator? Is it like an abacus?

Edited 7 September, 2012 by Whitey Grandad

[Ken Tone]

Jeez, I wasn't bragging I was just pointing out that I was never taught it! I have a degree too (Physic with Modern Computing) and I don't even remember any precedence rules in the maths I was taught doing that....

 

Funnily enough I was talking to a guy at work who is 23 and he knew about BODMAS.

 

And funnily enough your y^2 got me thinking about what we accept, cos if I see 3y^2 I take it as 3 * (y^2) not (3 * y)^2.

 

Reading the wikipedia article on it the bit that stick out for me is :-

 

 

 

BUT we're getting away here, because we're talking about algebraic notation, not a simple sum as first mooted in the thread, ie the diff between A+BC or A+B*C

 

So, for mine, the answer is 1, so there

 

Oh and try 1+2*3 using the calculator in Windows (if you use windows) in basic and scientific mode, former gives you 9, latter gives you 7. Not confusing in the slightest is it........

 

Not confusing at all. Plain wrong, which is the point I made about the rubbish calculator on phones etc before.

 

If you read the article you yourself posted it makes very clear that what amounts to BODMAS dates back centuries.

 

Beginning to rrealise what it must feel like to be MLG!

[Tokyo-Saint]

I don't have time to read all of this but needless to say I am happy to be alive and well.

 

Whitey, you sound kind and if I get lost again on the prices right or something, I am sure you will be able to save me.

 

Let me know what avatar you want me to have, the choice is now yours.

[Whitey Grandad]

I don't have time to read all of this but needless to say I am happy to be alive and well.

 

Whitey, you sound kind and if I get lost again on the prices right or something, I am sure you will be able to save me.

 

Let me know what avatar you want me to have, the choice is now yours.

 

That's very kind of you TS, I'll have to have a little think about this. There's a saying in chess that 'the threat is greater than the execution' so I'll leave it hanging over you if I may.

[PhilippineSaint]

That's very kind of you TS, I'll have to have a little think about this. There's a saying in chess that 'the threat is greater than the execution' so I'll leave it hanging over you if I may.

 

Bearsy's all ready hanging over the back of him

[Tokyo-Saint]

That's very kind of you TS, I'll have to have a little think about this. There's a saying in chess that 'the threat is greater than the execution' so I'll leave it hanging over you if I may.

 

I do that with my wife sometimes. No problem at all, just let me know.

[Wurzel]

Ditto. Without the brackets, you would do it in the order it's written, at least for the sake of those of us of more advanced years. I'm entirely happy with algebra, but why would some idiot leave off the brackets, unless it was deliberately to confuse everybody?

 

Jeez, I wasn't bragging I was just pointing out that I was never taught it! I have a degree too (Physic with Modern Computing) and I don't even remember any precedence rules in the maths I was taught doing that....

.

 

Glad to see it's not just me then. Maybe we all went to the same school.

[PhilippineSaint]

Glad to see it's not just me then. Maybe we all went to the same school.

 

that would be the one of hard knocks or like some on here Hardley educated

[Pugwash]

Glad to see it's not just me then. Maybe we all went to the same school.

 

P'raps I did too.

 

And it certainly was NOT Hardley (educated).

 

Just goes to show there are a number of different ways of teaching maths. I remember getting very upset at a new Junior School after being told by my new teacher that I had cheated by getting to the answers first. At that tender age I didn't quite understand the poor logic at arriving at that conclusion. Turned out I had been taught a different way to do the math.

[Pilchards]

Surely it should be a speed boat off the bullseye show?

 

 

did anyone ever win it in the end as it started to rust up towards the end of the series?

[The9]

May have been on here before, it was being discussed on radio yesterday and they said it was doing rounds on the internet.

 

6-1*0+2/2 = ?

 

Haven't read the rest of the thread sooooo.

 

BODMAS.

There are no brackets, so...

Division first 2/2 = 1

leaving 6-1*0+1

Multiplication next 1*0 = 0

leaving 6-0+1

then Addition 0+1 = 1

leaving 6-1

then subtraction = 5

 

That's my thinking anyway, though I could never remember what the "O" bit was in BODMAS, and it's not in that anyway...

[The9]

Reads rest of thread... Nice to see we've gone all Monty Hall in the meantime.

[Whitey Grandad]

I read the asterisk as an index. That's what computer programming does for you.

[The9]

I read the asterisk as an index. That's what computer programming does for you.

 

I don't even understand what the index thing is or was, but then I only got an A (there weren't any A* back then) in GCSE maths and chose to do PE instead of Additional Maths so I couldn't do the A Level.

 

Btw I am 39 and 3/4 (clinging on to my 30s) and was taught BODMAS in junior school, so that would have been around 1980-ish.

[Whitey Grandad]

I don't even understand what the index thing is or was, but then I only got an A (there weren't any A* back then) in GCSE maths and chose to do PE instead of Additional Maths so I couldn't do the A Level.

 

Btw I am 39 and 3/4 (clinging on to my 30s) and was taught BODMAS in junior school, so that would have been around 1980-ish.

 

I think it's because the asterisk is shown (on my IPad) as almost a superscript. This is the problem with mathematical notation and a limited character set. My BODMAS is more than twenty years older than yours and at that time nobody mentioned indices, or maybe they just hadn't reached eastern Essex at that time.

[Wurzel]

Haven't read the rest of the thread sooooo.

 

BODMAS.

There are no brackets, so...

Division first 2/2 = 1

leaving 6-1*0+1

Multiplication next 1*0 = 0

leaving 6-0+1

then Addition 0+1 = 1

leaving 6-1

then subtraction = 5

 

That's my thinking anyway, though I could never remember what the "O" bit was in BODMAS, and it's not in that anyway...

 

See now I'm even more confused. Seems the agreement is 7 is the correct answer so why is this wrong?

[Ken Tone]

See now I'm even more confused. Seems the agreement is 7 is the correct answer so why is this wrong?

 

THe9 goes wrong here --

leaving 6-0+1

then Addition 0+1 = 1

leaving 6-1

then subtraction = 5

..

because he is treating it incorrectly as if it were 6- (0+1). It isn't. It is 6-0+1, which is indeed 7. Even with BODMAS, additon and subtraction are ranked equallly , so you do read from left to right, and do the subtraction of 0 before the addition of 1.

 

6-1+0 = 5

6-0+1 = 7

6-(0+1) = 5

[Wurzel]

THe9 goes wrong here --

leaving 6-0+1

then Addition 0+1 = 1

leaving 6-1

then subtraction = 5

..

because he is treating it incorrectly as if it were 6- (0+1). It isn't. It is 6-0+1, which is indeed 7. Even with BODMAS, additon and subtraction are ranked equallly , so you do read from left to right, and do the subtraction of 0 before the addition of 1.

 

6-1+0 = 5

6-0+1 = 7

6-(0+1) = 5

 

So it's BODMAS or BODMSA then? Just the first being easier to remember as an acronym?

[Ken Tone]

So it's BODMAS or BODMSA then? Just the first being easier to remember as an acronym?

 

Or indeed BOMDSA

 

Younger children are mostly taught BIDMAS nowadays. I for 'index', ie powers, squares, cubes , etc. O stood for 'order', same thing, but im my view better because kids who did not yet understand powers, could be told O was for 'of' in the interim, as in "3/4 of" ,

 

but then, I'm an old fart.

[Jimbo]

Division comes firsy so, 2/2=1

Then i did 1*0= 0

Then i did 6-0+1=7

 

Isn't that 6-(0+1) therefore 5, given addition before subtraction?

[Whitey Grandad]

Isn't that 6-(0+1) therefore 5, given addition before subtraction?

 

No, there are no brackets in the original. The order of addition doesn't matter according to the commutative law.

[Deano6]

Are there really people in this world who think that 6-0+1=5, or has this thread just addled with a few brains?

 

 

How would they answer "If you have 6 oranges and take 0 away and then add another 1, how many do you have?"

[saintbletch]

No, there are no brackets in the original. The order of addition doesn't matter according to the commutative law.

 

I suspect Jimbo knew there were no brackets in the original but put them in to show the order he THOUGHT it should be evaluated in Whitey Grandad. And thanks, I knew there was a formal way of explaining it with through the commutative/associative/distributive laws. You're taking me back to Mr. Noonan's maths class in the 80s there.

 

Are there really people in this world who think that 6-0+1=5, or has this thread just addled with a few brains?

 

 

How would they answer "If you have 6 oranges and take 0 away and then add another 1, how many do you have?"

 

It appears that lots of people simply didn't learn about the priority of operators (or soon forgot it after their O Levels/GCSEs (other than with brackets)). (See what I did with the brackets there? Clever, eh? - by the way, how is that calculation for sexual achievement coming along?)

 

Isn't that 6-(0+1) therefore 5, given addition before subtraction?

 

Some of the subtleties of the BODMAS mnemonic haven't been explained Jimbo, so here, goes.

 

When you have a calculation like 6-1*0+2/2 the order in which you do the different steps is important - as the various answers on here have shown.

 

BODMAS provides that order. To your question about whether addition should be before subtraction, you're right it is confusing and it should more properly be written as

 

(B)(O)(DM)(AS) the Division and Multiplication are actually as important as each other - as are Addition and Subtraction. Which means when we have just multiplication and division in a part of a calculation, we do them from left to right. Same for addition and subtraction.

 

So when you look at the calculation 6 - 1 * 0 + 2 / 2, BODMAS effectively goes through putting in imaginary brackets for the symbols from B..O..D..M..A to S.

 

So we look for Brackets, but there is none.

We look for Orders (numbers raised to powers - i.e. 10 to the power 2 = 100, fractional powers - roots, etc.), but again there is none.

Then we look for Divisions and Multiplications - remember they have the same precedence so we can go from left to right.

 

So putting brackets around the Ds or Ms and the calculation becomes.

 

6 - (1 x 0) + (2 / 2)

 

Which is the same as

 

6 - 0 + 1

 

So as we're left with only the A and S of BODMAS, and we know they are the same priority, we can simply evaluate the calculation from left to right.

 

Which is how you get to Deano6's 6 oranges take away no oranges and add one more orange.

 

So we get the answer -9 oranges. Well we've had every other answer on this thread.

[Whitey Grandad]

As a good accountant would say, what answer would you like?