Hey Veeky Forums, I'm shit at math so I was hoping you guys could help me grasp probability...

Hey Veeky Forums, I'm shit at math so I was hoping you guys could help me grasp probability. I contrived a word problem but have no idea how to solve it.

> Guy A asks Guy B to guess a 3-letter acronym, what is the mathematical likelihood Guy B will guess all letters correctly in order? What about out of order? Guy A tells him the first letter, what would the probability be now?

Even to me it's obvious if it was just 1 letter it would be 1/26, but what about 2? Is that 26x26? What about 3 or 4 letters, and so on? Are there x-factors, do they stack?

*buhuuurp* Just lick my balls, Mharti

Weed need to go *buuuuurp* back to *baarp* da future.

How many letters does the alphabet have which the guy is using to create this acronym?

Out of order you have combinations
with order you have permutations.

>Guy A asks Guy B to guess a 3-letter acronym, what is the mathematical likelihood Guy B will guess all letters correctly in order?

Let's say the acronym is ABC. The chance of guessing A first is 1/26, B second is 1/26, and C third is 1/26. If you multiply them together, (1/26)^3 is 1/17576.

>What about out of order?
Now, there are 6 possible orientations of ABC, which are: ABC, ACB, CAB, CBA, BAC, and BCA (this can be calculated using 3!). Since there are 6 times more orientations, you multiply 1/17576 from the answer by 6.

>Guy A tells him the first letter, what would the probability be now?
Since A is a given, and order still matters, the probability of guessing B and C in order are both 1/26. So, (1/26)^2 is 676.

Assuming no extra information like what combinations that are not acronyms:

For each letter space in the acronym there are 26 possible combinations so in total there are 26*26*26 possible 3 letter combinations,which would be 17576.

To guess them in order that means that he would need to fine the single one combination that matches the acronym guy A is talking about so 1/17576

To guess them out order he would simply need to find the three letters and order in one of the possible ways, which would be 3 factorial or six. Therefore to guess it out of order the chances are 6/17576

If the guy is told the first letter then in order it would be 1/676 and to get them in any order it would be 2 factorial out of 676 so 2/676

ez pz. From the way I've laid it out you can probably generalize on your own.

Thanks for the help, Veeky Forums

Is Doc and Mharti scientifically accurate?

> like what combinations that are not acronyms
What does this mean? And why did you use the factorial?

>What does this mean?

Well, maybe a problem will have rules as to what constitutes a proper acronym. Imagine if the problem were to be about words. 'bow' is a 3 letter word but 'wwz' is not a 3 letter word, as it is not even a word. In the problem I am just assuming that there are no rules that limit the possibilities.

>And why did you use the factorial?

Because imagine if the acronym is XYZ. To get these out of order correctly you could guess YZX or YXZ, etc. Those are 3 letters so you want to find out how many ways are there to 'order' three obejcts, and that is exactly what the factorial defined over the naturals does.

It is just a function. You could also find all the combinations by hand but why do that when mathematicians already solved this problem.

number of possible desired outcomes / number of all outcomes


how many different ways are there to pick 3 letters from 26

ordered -> 26 P 3

unordered -> 26 C 3

so the probability of picking a winning premutation is 1/(26 P 3)

fuck combinations though

Your shit is as bad as those pedophile cartoons. Fucking degenerate

Yeah, the probability tree is how I remember learning in elementary, then we did simple stuff like coin tosses. In high school most of the math/science department resources were poured into the AP classes so we either had math teachers in their first year or some old guy that kept saying he was in Mensa, talking about graduating university in his teens, and just being old. So on one hand I was great in English, law, foreign languages and everything besides math; on the other I can't math worth a shit and saw people I thought were smarter than me taking applied grade 11 classes in grade 12.

So if the acronym was 4 letters, the factorial would be 24. And it would be 1/456976 or 24/456976, right?

Thanks bro, I appreciate the support.

What does the P and the C mean? How do I apply them?

People of Veeky Forums who are smarter than me, I have a fucking weird question.

From the answers before, if we generalize the formula to calculate the 'out of order' probability for an n-size acronym is:

[math]\frac{n!}{26^n}[/math]

But this has some interesting properties, namely that the factorial function grows faster than the exponential function. Which means that there exists some non trivial solution for the equation: (0 being the trivial solution)

[math]\frac{n!}{26^n} = 1[/math]

And after using some log identities and computing, the answer is

[math]n=67.5797[/math]

So what would this mean? If we have a 68 letter acronym, the probability of guessing it right is 100% (actually, like 150% for 68 letters).

How is this possible? If the acronym is bbb...b and I guess aaa...a then I would be wrong.

How come?

Another thing is that the limit to infinity of the expression is infinity. Which means that you have a 100% chance of guessing an infinite acronym.

But what if the acronym is aaaaaa...

I could guess bbbbbb... and I would be fucking wrong.

What just happened to probability right now? Did we break the universe?

Go back to your containment board
Fucking degenerate.

...

Bumping.

Can a nigga get an answer?

I mean can?

Can a nigga get an answer?

fucking degenerate

If you are not a degenerate then explain why probability breaks down for n larger than 67

JUST FUCK OFF MODS BAN THIS PIECE OF PEDOSHIT

I'm not even OP though... what the fuck.

It breaks down because the formula is wrong, obviously

But it isn't. For n=3 the formula for the 'in any order' is 3! / 26*26*26 = 6/17576 = 0.03%

And that makes sense. There are 17576 possible outcomes and only 6 desired outcomes.

If you are saying the formula is wrong then you are saying that the probability for OP's question is not 6/17576 so I hope you have the alternate supposedly correct answer.

It's wrong because the right answer depends on whether the acronym allows repeated letters or not. And in either case, you won't get n!/26^n anyway

And to add to that, you can clearly see the formula is wrong because in the denominator, you have 26^n - which means you've allowed repetition, whereas in the numerator you have n! - which means you've assumed the letters are distinct

Wew, you are right. Shit.

But okay, hear me out. I can still construct an example where this happens.

Consider a written language that has 5000 characters. Now consider acronyms that do not allow for repetitions at all, every character just once.

The general formula here would indeed be (for an n sized acronym)

[math]\frac{n!}{5000^n}[/math]

And through the same methods I found that the solution for

[math]\frac{n!}{5000^n} = 1[/math]

is
[math]n = 1969.45 [/math]

So if you were to guess an acronym of length 1970, you would have a probability larger than 100%.

How is that even possible?

Once again, 5000^n is wrong. The correct denominator, in this case, would be 5000*(5000-1)*(5000-2)*...*(5000 - n + 1)

Think of it like this: You have n boxes and 5000 objects. The first box can be filled in 5000 ways - after you've done that, the next one can be filled in 4999 ways, and so on until you get to the last box which can be filled in 5000 - n + 1 ways.

You would get 5000 in the denominator only if you assumed that you have at least 5000 copies of each object to begin with.

And you probably made a calculation error. 1970!/(5000)^1970 < (1970)^1970/(5000)^1970 < 1