MATH questions - It has begun once again!

[4RM3D]

It has been a while since we had a good mathematics thread. I'll start with clearing a few 'known' misconceptions; the ones I can remember, at least. Feel free to add your own. Also, if you are interested you can try and see if you can answer all of them correctly.

First a question of my own making. It started out to joke around with friends, but I noticed most couldn't answer the question correctly.
0.1 * 0.1 = ?

Spoiler

0.01 | Yes, nothing special, no trick question.

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 * 0 = ?

Spoiler

9 | You do multiplications first. So you get 1 * 0 = 0 and then 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1

You got a product that costs $100. How much does the product cost without 20% tax (VAT). (Yes, tax is not the same in every country. But for the sake of this question the tax is 20%)

Spoiler

$83.33 | No, not $80. When you subtract tax, you have to add the tax percentage to the total. So $100 is 120% (not 100%), thus $100 / 120% * 100% = $83.33 (mathematically the syntax is incorrect, but you get the point)

You have 2 separate events (triggers) that can happen simultaneously. Each event has a 50% chance of happening. What is the chance that event 1 or event 2 or both happens?

Spoiler

75% | It is not 50% + 50% = 100% For starters you can't add the two possibility, unless they are mutually exclusive.
There is a 50% * 50% = 25% chance that both events occur at the same time (and there is a 25% chance none of them occur at the same time).
But what about either one? For that you have to remove the possible overlap, which is 25%. Thus (50% + 50%) - (50% * 50%) = 75% For completion sake the mathematical formula: P(A or B) = P(A) + P(B) - P(A and B)

And finally, onward to the last question.
A women gives birth to twins. One of them is a boy. What is the chance the other one is a boy also? (Excluding biological factors and statistics)

Spoiler

TWO | Wait...what? 2 what? There are 2 possible answers depending on your interpretation. If you thought 33.33% or if you thought 50%, then you are right. But an even better answer is: It is either 33.33% or 50% [http://en.wikipedia.org/wiki/Boy_or_Girl_paradox] depending on how you look at it.

 

[SckizoBoy]

... yeah... next time, give us something proper by way of questions, like game theory or differential equations, or even geometry, ffs!

 

[4RM3D]

... yeah... next time, give us something proper by way of questions, like game theory or differential equations, or even geometry, ffs!

Geometry you ask?

There is an alley 2 meters width with 2 ladders. One ladder is 4 meters long and is leaning against the right wall from the left corner. The other ladder is 5 meters long and is leaning against the left wall from the right corner. Meaning each ladder forms a triangle (ground, wall, ladder). At which height do the ladders cross each other?

 

[Catfood220]

I hate maths, I can do enough to get by but you all might as well be speaking Japanese for all the sense it makes to me.

 

[4RM3D]

Too easy!

Where are the calculus problems like differentiation and trigonometric ratios?

Hmmmm, can't think of anything ATM. But I will not leave you empty-handed.

You have the numbers 1 through 19. You have to use all of them once. If you add the numbers horizontally or diagonally they have to have the same result.

I can not draw the diagram here, so I'll explain how it looks like...

You have 5 rows:
1) row of 3
2) row of 4
3) row of 5
4) row of 4
5) row of 3

So, it's basically a double symmetrical pyramid.

Can you solve it?

 

[SckizoBoy]

... yeah... next time, give us something proper by way of questions, like game theory or differential equations, or even geometry, ffs!

Geometry you ask?

There is an alley 2 meters width with 2 ladders. One ladder is 4 meters long and is leaning against the right wall from the left corner. The other ladder is 5 meters long and is leaning against the left wall from the right corner. Meaning each ladder forms a triangle (ground, wall, ladder). At which height do the ladders cross each other?

Quick working but not sure... 1.973m

And that's more algebra than geometry, isn't it!? -_-

 

[4RM3D]

EDIT: All right, I'll add my own . . .

A flag pole casts a shadow 5 metres long, the angle of the sun's elevation is 60 degrees above the horizon.

How tall is the flag pole?

Spoiler

2.8868 meters

...I think, still double checking.

EDIT: formula --> 5 * TAN(((90 - 60) * Pi) / 180)

 

[4RM3D]

EDIT: formula --> 5 * TAN(((90 - 60) * Pi) / 180)

No, it's the tan of the angle multiplied by the adjacent.
So it's just 5 * tan(60)

Spoiler: so it's roughly

8.66 metres

5 * TAN(60) = 1.6

8.66 = 5 / TAN(((90 - 60) * Pi) / 180)

Meanwhile, I'm struggling with the pyramid problem :/

You don't understand the question or you can't solve it (yet)?

 

[4RM3D]

Your calculator (or google) is in Radians mode. You need it to be in Degrees mode.
(Compare those two search results.)

Ah, yes. I've totally forgotten about that. It has been a while since I worked with tangents.

It's a bit like Sudoku yes?

I'm terrible at sudoku.

It is like Sudoku, but worse. XD

 

[4RM3D]

Quick working but not sure... 1.973m

And that's more algebra than geometry, isn't it!? -_-

I am interested to see how you reached that number. I thought it was around 2.1m, but it has been a while since I've asked the question.

 

[SckizoBoy]

Quick working but not sure... 1.973m

And that's more algebra than geometry, isn't it!? -_-

I am interested to see how you reached that number. I thought it was around 2.1m, but it has been a while since I've asked the question.

I did it by describing the two ladders as lines in cartesian co-ordinates (4m ladder ascending left to right, 5m ladder ascending right to left).

So:

4m grad = root3
from origin

5m grad = -(root21)/2
from root21

subbed in the x term and had a result of 2(root21) over (2 + root7) as the y-coord of the intersect.

Anyway, thanks to you, I didn't fall asleep at work!

 

[isometry]

Title should have been "Arithmetic questions." Arithmetic is to math as letters are to literature.

And finally, onward to the last question.
A women gives birth to twins. One of them is a boy. What is the chance the other one is a boy also? (Excluding biological factors and statistics)

Spoiler

TWO | Wait...what? 2 what? There are 2 possible answers depending on your interpretation. If you thought 33.33% or if you thought 50%, then you are right. But an even better answer is: It is either 33.33% or 50% [http://en.wikipedia.org/wiki/Boy_or_Girl_paradox] depending on how you look at it.

No, I disagree with this entirely. The second event is completely independent of the first, it's just 1/2. That's the first thing they teach you in probability, that just because you flipped a coin and got heads doesn't mean that if you flip another one it's more likely to come out tails. The Wiki page describes something completely different.

I agree with SirBryghtside, of course. Note the wiki page is tagged with "this page may involve original research", which is often a sign of cranks. The correct answer is 50% because we are given that the first child is a boy. If the poster wanted to make the question ambiguous they would need to do a better job wording it differently.

 

[4RM3D]

Anyway, thanks to you, I didn't fall asleep at work!

Lol. Well, glad to be of service.

*snip*

*snip*

Oh really? I might have phrased it wrong then. But as I understand it, it is as follows:

A) A women gives birth to twins. One of them is a boy. What is the chance the other one is a boy also?

Thus having the following possibilities:
boy - girl
boy - boy
girl - boy
girl - girl

Meaning there is 1/3 chance of another boy.

B) A women gives birth to twins. The first one is a boy. What is the chance the second one is a boy also?

Thus having the following possibilities:
boy - girl
boy - boy
girl - boy
girl - girl

Meaning there is 1/2 chance of another boy.

Tell me where I am wrong?

 

[Vegosiux]

A) A women gives birth to twins. One of them is a boy. What is the chance the other one is a boy also?

Thus having the following possibilities:
boy - girl
boy - boy
girl - boy
girl - girl

Meaning there is 1/3 chance of another boy.

B) A women gives birth to twins. The first one is a boy. What is the chance the second one is a boy also?

Thus having the following possibilities:
boy - girl
boy - boy
girl - boy
girl - girl

Meaning there is 1/2 chance of another boy.

Tell me where I am wrong?

In calling it a "math question" while it's actually a "biology question". I have no idea what ratios monozygotic and dizygotic pregnancies have as far as twin pregnancy is concerned, and that's a crucial piece of information we need.

Monozygotic twins virtually have a 100% chance of being the same sex (it IS possible to have different sexes that way, but it's exceedingly rare), and all, but I don't see a reason to assume that we have a 50% chance for a twin pregnancy to be monozygotic or dizygotic.

I do believe that dizygotic twins are a lot rarer than monozygotic ones, therefore I'd say the probability that the other twin is also a boy is much higher than 50%, but as I do not know the ratios for real, that is just an assumption on my part.

 

[SaikyoKid]

*snip'd*

I can kinda see what you're trying to get at, but Sir and Iso are right. 50 percent is the only right answer. In your A example, you're considering there being 4 separate answers. In reality though, your third and first answer are really just the same thing. I can see you're kinda trying to word it differently to make it work out that way, but I'm afraid it just doesn't cut it.

 

[Chairman Miaow]

And finally, onward to the last question.
A women gives birth to twins. One of them is a boy. What is the chance the other one is a boy also? (Excluding biological factors and statistics)

Spoiler

TWO | Wait...what? 2 what? There are 2 possible answers depending on your interpretation. If you thought 33.33% or if you thought 50%, then you are right. But an even better answer is: It is either 33.33% or 50% [http://en.wikipedia.org/wiki/Boy_or_Girl_paradox] depending on how you look at it.

No, I disagree with this entirely. The second event is completely independent of the first, it's just 1/2. That's the first thing they teach you in probability, that just because you flipped a coin and got heads doesn't mean that if you flip another one it's more likely to come out tails. The Wiki page describes something completely different.

Exactly what I thought.

 

[Vegosiux]

And finally, onward to the last question.
A women gives birth to twins. One of them is a boy. What is the chance the other one is a boy also? (Excluding biological factors and statistics)

Spoiler

TWO | Wait...what? 2 what? There are 2 possible answers depending on your interpretation. If you thought 33.33% or if you thought 50%, then you are right. But an even better answer is: It is either 33.33% or 50% [http://en.wikipedia.org/wiki/Boy_or_Girl_paradox] depending on how you look at it.

No, I disagree with this entirely. The second event is completely independent of the first, it's just 1/2. That's the first thing they teach you in probability, that just because you flipped a coin and got heads doesn't mean that if you flip another one it's more likely to come out tails. The Wiki page describes something completely different.

Exactly what I thought.

*sigh* In case of twins, the gender of one is not necessarily independent of the gender of the other, as in a monozygotic pregnancy the sexes are the same in virtually 100% of cases. In case of two children from two different pregnancies it IS, but in case of twins, it is not.

 

[Chairman Miaow]

And finally, onward to the last question.
A women gives birth to twins. One of them is a boy. What is the chance the other one is a boy also? (Excluding biological factors and statistics)

Spoiler

TWO | Wait...what? 2 what? There are 2 possible answers depending on your interpretation. If you thought 33.33% or if you thought 50%, then you are right. But an even better answer is: It is either 33.33% or 50% [http://en.wikipedia.org/wiki/Boy_or_Girl_paradox] depending on how you look at it.

No, I disagree with this entirely. The second event is completely independent of the first, it's just 1/2. That's the first thing they teach you in probability, that just because you flipped a coin and got heads doesn't mean that if you flip another one it's more likely to come out tails. The Wiki page describes something completely different.

Exactly what I thought.

*sigh* In case of twins, the gender of one is not necessarily independent of the gender of the other, as in a monozygotic pregnancy the sexes are the same in virtually 100% of cases. In case of two children from two different pregnancies it IS, but in case of twins, it is not.

but that still wouldn't be 33% surely? and it said ignoring biological factors and statistics. no need to be patronising.

 

[isometry]

Anyway, thanks to you, I didn't fall asleep at work!

Lol. Well, glad to be of service.

*snip*

*snip*

Oh really? I might have phrased it wrong then. But as I understand it, it is as follows:

A) A women gives birth to twins. One of them is a boy. What is the chance the other one is a boy also?

Thus having the following possibilities:
boy - girl
boy - boy
girl - boy
girl - girl

Meaning there is 1/3 chance of another boy.

B) A women gives birth to twins. The first one is a boy. What is the chance the second one is a boy also?

Thus having the following possibilities:
boy - girl
boy - boy
girl - boy
girl - girl

Meaning there is 1/2 chance of another boy.

Tell me where I am wrong?

Where it goes wrong is in the step where you use the information "one kid is a boy" to cross out one possibility and divide the probability up on the remaining possibilities.

To start with the distribution is an equal chance of four possibilities:

boy - girl , 25%
boy - boy , 25%
girl - boy , 25%
girl - girl , 25%

I wrote "25%" next to each because that's the chance of that event. Now when you find out the first one is a boy, what you did is this:

boy - girl , 33%
boy - boy , 33%
girl - boy , 33%
girl - girl , 0%

The correct answer is this:

boy - girl , 25%
boy - boy , 50%
girl - boy , 25%
girl - girl , 0%

How do we get this answer, how do we know it's correct? It comes from Bayes theorem. First, let A and B be two events with probabilities P(A) and P(B). The notation P(A|B) means "the probability that B happens, given that A happens." Bayes' theorem says:

P(A|B) = P(B|A)P(A)/P(B)

To apply it to the case at hand we have:

A = "both kids are boys"
B = "one of the kids is a boy"

Therefore the thing we want to estimate is P(A|B), the probability that both kids are boys given that one of them is a boy. Let's look at the terms in Bayes theorem:

P(A) = the probability both kids are boys = 1/4

P(B) = the probability one of the kids is a boy = 1/2

P(B|A) = the probability that one kid is a boy, given that both are boys = 100%

Plug this into Bayes theorem and we get:

P(A|B) = (1.0)*(.25)/(0.5) = 1/2 = 50%

So, the probability that both kids are boys, given that one of them is a boy, is 50%. The "cross out possibilities that don't happen and split the probability equally on the others" approach only works if the events are independent, and in this case they are not.

 

[Palademon]

... yeah... next time, give us something proper by way of questions, like game theory or differential equations, or even geometry, ffs!

I started differential equations today.

I would've been all like "COME AT ME BRO!"