1/1000 enemies drop loot. You have an item which will tell you

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>math

>>384815839
How many enemies does the item examine?

>>384818560
a lot
>>384815839
>Nine
wrong
It's either 100 or 99

>>384818560
That is not important or strictly needed, although you may find it useful to imagine it is and examining an amount you come up with

>>384819216
>It's either 100 or 99
Why?

>>384815839
91?

>>384819362
Because the chance is 99%
You have 1% chance it's not there.


and let's say the error accumulate (Which I don't know how would work in this case )
0.01 +100=1
So you will miss 1 out of 100

The truth is that it can be anywhere from 0-100
1/1000 enemies drop loot. You don't need this information it will only tell you how much enemies the thing scanned

>>384819849
>0.01 +100
I mean *

>>384815839
It depends on the base examined of enemies, since you said [answer] I'd guess you looked at 100,000

>>384815839

The entire 1/1000 enemies drop loot doesn't matter in the equation.

You have a machine with 99% accuracy, which claims it found a 100 targets with loot. This means you can expect at least 99 have loot.

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>>384819849
Most of these images with Kurisu are memes, so this baka I guess ?

>>384819849
>Because the chance is 99%
Afraid not
You DO need the base rate of 1/1000 drops since it tells you how many of those 100 enemies are false positives.
It can be anywhere between 0-100 yes although the expected value (to nearest whole number) is the average and only has one answer

>>384820013
>It depends on the base examined of enemies
It does not

>>384820364

Then either the accuracy of the machine isn't 99% or the drop rate isn't 1/1000. It can't work both ways.

>>384815839


>You have an item which will tell you if an enemy is going to drop loot.
>99% of the time when it examines an enemy it correctly says whether or not they have loot

>It examines random enemies and finds 100 that it thinks have loot, what is the expected number of loot items from them?

Since the item is correct 99 out of 100 times and have found 100 enemies it thinks has loot, assuming that one monster carries either one piece of loot or none, one can expect to find zero to 100 pieces of loot.

like 50

>>384820509
Are you saying it is physically impossible for a dev to make a game where an enemy has a drop rate of 1/1000 and the game has an item which correctly identifies whether or not an enemy will drop, but only 99% of the time?

>>384815839
In reality none of them could have loot, but given the machine's 99% accuracy and the 1/1000 probability being irrelevant you should expect about 99 of the 100 monsters to have loot.
>>384820364
Unless I'm misunderstanding the question the 1/1000 enemies having loot doesn't matter at all. The rate of false positives due to the machine's inaccuracy is 1%. The 1/1000 enemies doesn't matter if the machine already found 100 enemies that supposedly have loot

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>>384820364
>You DO need the base rate of 1/1000 drops since it tells you how many of those 100 enemies are false positives.
Can you explain ?

I imagine he scanned 100,000
>it examines random enemies
and said that 100 are the ones.
that's it.

>>384815839
thats a probability conjunction of 2 events. too lazy to do it, someone find a calculator on google

>>384820828
>>384820839
>Unless I'm misunderstanding the question the 1/1000 enemies having loot doesn't matter at all
Base rate fallacy really isn't hardwired into the human brain and literally everyone gets this wrong at first.
If there are 1000 enemies, we can expect 1 to have loot.
The item correctly finds an average of 1 * 0.99 = 0.99 true positives
Of the 999 without loot, it is wrong on 0.01% of them, giving 999 * 0.01 = 9.99 false positives

So the item finds on average 0.99 true positives and 9.99 false positives. A total of 10.98 positives, of which 0.99 are true.
So when the item says an enemy has loot, it is only correct 0.99/10.98 = 0.09 (9%) of the time, because the times when it is correct is swamped by how many false positives it picks up.
So with 100 enemies it says has loot, you can expect 100 * 0.09 = 9 enemies that truly have loot

>stat booster item is dropped rng
>stat booster item effect is based on rng

>>384820267
But it can scan an enemy that doesn't have loot and report that it does.

>>384815839
It's nine. Suppose it examines 1000 enemies, out of those 1000, on average it will find 11 that it thinks they have loot (10 + 1, where 10 is the margin of error, i.e. 1% of 1000, and 1 is the enemy with actual loot). Multiply this by 9, and out of 9000 mobs on average 9 will have actual loot and 90 will be false flags, and this gives us 99 examined enemies.
We can deduce that for every X examined enemies that the item thinks they have loot, then the number of enemies with actual loot is X/11, so for 100 enemies 100/11 is approximatevly equal to 9.

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>>384821467
Thanks for the quick rundown. I get it now.
I guess I'm just retarded

>>384820509
>>384820828
>>384820364
Wanna know how I know you've never taken a statistics and probability course?

https://en.wikipedia.org/wiki/False_positive_paradox
https://www.youtube.com/watch?v=R13BD8qKeTg

I was about to type a long explanation but >>384821467 is the gist of things.

>>384815839
99
Doesn't matter if only 1/1000 enemies drop loot because the item has found 100 enemies with a 99 % chance of them having loot.

>>384822049
Don't feel too retarded, other than statisticians, doctors are probably the most common profession to encounter these kind of problems with disease rates and testing and I guarantee most of them don't know how the base rate affects testing.

Also if Trumpy wants to test for terrorists he has to either not care and not act about false positives (like the complete travel ban fair enough) or if he wants to not get false positives then make the test really really really accurate (bc the base rate of people being terrorists is so low)

>>384822284
It does matter because the low probability of having loot means that the item would produce more false positives than true positives. Basically the item will falsely predict 1 out of 100 enemies to have loot when in reality only 1 out of 1000 enemies have loot. That means in a group of 10 positive results, we'd expect only 1 of them to actually have loot.

>>384821467
There are 100 enemies the item thinks have loot, not 1000. Since the item is right 99% of the time you can expect from zero to 100 loot items from those 100 enemies.

>>384822585
But the OP said when it scanned an (to us) unknown number of enemies the item found 100 of those enemies which hold loot. The low probability seems like a red herring. Explain to me why it isn't.

>>384822864
The specific wording about how often it is right is important.
If an enemy does have loot then it says it does 99% of the time
If an enemy doesn't have loot then it says it doesn't 99% of the time

That doesn't mean that when it says these 100 enemies have loot that 99% of them do, they will be a mix of enemies that do and enemies that don't since it can include false positives and true positives. The mix is determined by how likely it is for a random enemy to have loot, that is the 1/1000

>>384823694
But in the end you have 100 enemies.
You can calculate the probability of 100 pieces of loot, 50 pieces, 1 piece and so on but you can expect from zero pieces (the item was always wrong) to 100 (the item was always right).

.99 * 1 + .99 * 1 + ... = .99 (1 + 1 + ...) = 99

>>384824175
I should add that this is the expected number, in game it could be from 0 to 100.

>>384823642
>The low probability seems like a red herring. Explain to me why it isn't.
I already did. The rate of false positives is higher than the incidence rate. 0.1% of the population has loot, but the item will identify 1% of the population as having loot. The problem is you're confusing accuracy with probability. The item saying an enemy has loot with a probability of 99% doesn't mean the enemy has a 99% chance of having loot, it means out of 100 enemies, 99 of them will be correctly labeled. Again meaning that out of 100 enemies with no loot, 1 will be labeled as having loot. But the incidence rate is 1 out of 1000. So out of 1000 randomly chosen enemies, 1 will have loot. Out of the rest of the 999 enemies the item will incorrectly identify 9.99 or 10 enemies as having loot. That means only 1 out of 11 enemies actually have loot. The real red herring is the "unknown number of enemies scanned".

Watch this if you want to know more:
https://www.youtube.com/watch?v=R13BD8qKeTg

>>384823642
The low probability just ensures that the answer is a more counter-intuitive low number 9 instead of something closer to 99/100 but it doesn't have to be low, although it makes the effect of the base rate more pronounced

Imagine if the item was only correct at identifying those that do/don't 50% of the time with a 10% drop rate
Out of 200 enemies 20 have loot and 180 don't
On average it thinks 100 of them has loot, but that's from it correctly finding half of those that do and incorrectly finding half of those that don't
50% * 20 + 50% * 180 = 10 true + 90 false = 100
So it has found 100 enemies that it THINKS has loot but only 10 of those ones ACTUALLY do. So when it tells you
"this enemy will drop loot"
It is only correct 10% of the time, different kind of accuracy from
"If this enemy has loot, the item is right 50% of the time"

False positives get recorded the same as true positives, and since the drop is so rare there are more false positives than true positives unless the item is really really accurate

>>384824146
Generally in stats qs when it asks for an expected value it means what do you expect on average, obviously any number between 0 and 100 is possible

>my fucking face when i get it
>i dont have one

>>384819265
Yes it is, 1% of those that it said wouldn't drop loot should.

>>384824772
The item in the OP has already found, with 99% accuracy, 100 enemies which carry loot. It does not matter how often loot occurs because the item has already found 100 enemies fitting the bill and 99 times out of 100 we can be sure that one of the enemies out of the 100 carries loot.
I don't get where you're aiming at with how high the probability is that an enemy carries loot because the item has already determined 100 enemies that do. What we can expect is that zero enemies actually carry loot, that 100 enemies actually carry loot or any number in between.

>>384824772
Not him but after seeing the video I get it.

>>384825064
The OP states that the item has a 99% chances of determining if an enemy does or does not have loot. The item analyzes random enemies until it finds 100 enemies that carry loot.
It's not that it can determine it at a rate of 99% if the enemy has loot, it can determine it wether the enemy has loot or not.

>>384825470
>I don't get where you're aiming at with how high the probability
Because as I said before, the rate of false positives is 10x greater than the number of enemies that actually have the loot.
>99 times out of 100 we can be sure that one of the enemies out of the 100 carries loot.
No no no no no no no. The item has already been used to label those 100 enemies. We cannot then "reuse" the item on those 100 to assume that 99 of them will be correctly labeled. You're being very jumbled and mixed up.
> What we can expect is that zero enemies actually carry loot, that 100 enemies actually carry loot or any number in between.
Again no. "Expect" has a very specific meaning in statistics/probability. It means, to put it simply, what is the average value we get if we repeat the experiment an unlimited number of times. Read
https://en.wikipedia.org/wiki/Expected_value
0-100 are "possible" values but not expected values.

scan 100,000 enemies (for example)

100 of them have loot (1 / 1000)

99% scan success rate, so 99,000 are correctly scanned

of these, 99 have loot, the rest dont (99,000 - 99 = 98,901 dont have loot)

for the final thousand, the scanner gives the opposite reading (given in the problem)

in reality, 1 of the final thousand has loot, and 999 dont

the scanner will say that 1 doesnt, and 999 do

this brings the total "loot" rate to 999 + 99 = 1098

total "no loot" rate to 98,901 + 1 = 98,902

add them together, 100,000 (just to check)

1,098 / 100,000 total scanned = .01098

so for any given number of enemies scanned, the number the scanner give you will be .01098 times it (actual loot is .001 times # enemies)

if the scanner gives you the number 100...

.01098x = 100

x = 100 / .01098

x = 9,107.4~

Didn't really double check much. Will program a simulation real quick if I feel like it. Feel free to discuss

>>384825904
Can you be more specific about what you think the difference is between
>the item has a 99% chances of determining if an enemy does or does not have loot
and
>it can determine it at a rate of 99% if the enemy has loot

The second quote starts the same as the first but without the
>or does not have loot

>>384826265
wait, shit, I thought the question was asking how many enemies were scanned. well the logic and everything still holds, and now that the number of enemies scanned is known, the answer should be simple

actual loot chance is .001 * numEnemies

.001 * 9,107.4 = 9~

>>384815839
Random sample of 1000 monsters has 1 enemy with loot and 999 without. Run it through scanner and you will get 9.9 enemies without loot and 0.9 enemy with loot all marked as proper targets. Therefore the rate of scanner is something like 110 to 1. That would actually put the actual rate of item bearing monsters as 0.009 in scanned positive group. That would mean there is actually 0.9 expected loot item to drop in a sample of 100.

>>384827149
Well a small error in calculations, logic is still good.

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Well, /v/?

>>384827578
50

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>>384827578
50
You can't fool me there, I've just seen video on this.

Easier one

A particular enemy is extra weak, it has a much smaller life bar than all the enemies you've currently met, has only one arm, half a leg and basically your fucking stupid.
Which is more likely?
1. This is a boss enemy
2. This is a boss enemy and you are able to kill him in a single hit

>>384826091
Fuck I think I get it now.
Fucking counter-intuitive logic is hurting my brainlet.

kurisu is a cutie

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>>384827578
The question is too vague since there aren't enough parenthesis but if there are two operations with equal priority according to PEMDAS, I've always been taught to go left to right. 20/2*5 = 10*5 = 50

>>384827991
3. It's just the first form and will fuck you up in 2nd form. The 3rd form will be easy but drawn out.

>>384827578
2

If you drop the multiplication sign you are always implying the two numbers are actually a part of one "word". In fact generally you use division and multiplication signs to SEPARATE things. If you want to read it as 20/(4-2)5 you just put it as a fraction.

>>384815839
A given enemy has a:
999/1000 chance of nodrop
1/1000 chance of loot

which is split up into:

99/100,000 chance of loot, true positive
1/100,000 chance of no loot, false negative
98901/100,000 chance of no loot, true negative
999/100,000 chance of loot, false positive

Given that your detector ~thinks~ the enemy has loot, then:
It's a 99/1098 chance they do have loot,
and a 999/1098 chance of a false positive.

So yes, out of 100, you'd expect 9 to be correct, and 91 to be false positives.

Let's define the following events:
D = Event where item detects that some enemy has loot
L = Event where some enemy truly has loot
C = Event where the item correctly indicates whether or not some enemy has loot

>It examines random enemies and finds 100 that it thinks have loot, what is the expected number of loot items from them?
So the key to this problem is determining Pr(L | D), then the expected number of loot items is simply 100*Pr(L | D)

>1/1000 enemies drop loot.
Pr(L) = 0.001
Pr(~L) = 0.999

>99% of the time when it examines an enemy it correctly says whether or not they have loot
P(C) = Pr(D and L) + Pr(~D and ~L) = 0.99
P(~C) = Pr(D and ~L) + Pr(~D and L) = 0.01
In other words:
P(C) = Pr(L)*Pr(D | L) + Pr(~L)*Pr(~D | ~L) = 0.99
P(~C) = Pr(~L)*Pr(D | ~L) + Pr(L)*Pr(~D | L) = 0.01

So:
Pr(L | D) = Pr(L and D)/Pr(D) = Pr(D and L)/Pr(D) = Pr(L)*Pr(D | L)/Pr(D)
Pr(D) = Pr(D and ~L) + Pr(D and L) = Pr(~L)*Pr(D | ~L) + Pr(L)*Pr(D | L)

Pr(L | D) = Pr(L)*Pr(D | L)/(Pr(~L)*Pr(D | ~L) + Pr(L)*Pr(D | L))

So we know the numeric values of Pr(L) and Pr(~L), however, we do not know the individual numeric values of Pr(D | L) or Pr(D | ~L), all we know is that Pr(L)*Pr(D | L) + Pr(~L)*Pr(~D | ~L) = 0.99 and Pr(~L)*Pr(D | ~L) + Pr(L)*Pr(~D | L) = 0.01, so we can't come to a numeric answer to your question.

>>384828508
To follow up on this, I think a lot of people here are making the false assumption that Pr(D | L) = Pr(~D | ~L) = 0.99 and that Pr(D | ~L) = Pr(~D | L) = 0.01, which is not implied anywhere in the problem statement, strictly speaking.

>>384815839
99

>>384828086
That's true

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>>384826265
>>384827003

averaging 1k runs

>>384831645
Nice

Well just some shitty math:
If the item is correct 1% of the time, and only 0.1% of all creatures actually have loot, then you would expect that in a set of creatures expected to have loot that only ~1/10 of them will actually have loot.

The answer is probably around 10.

There are four cards that have a letter written on one side and a number on the other side

A man tells you that "Even numbered cards must always have vowels on the other side"

The four cards in front of you show
O N 4 1

Turning over as few cards as possible, which cards do you need to turn over to see if the the man is true?

>>384815839
now go and solve some puzzles
https://layton.world

>>384815839
99

>>384833016
1

>>384834860
It's N and 4

>>384834960
forgot . I meant O(first) but guess I was wrong.

>>384815839
B A Y E S
A
Y
E
S

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>>384833016
Here's a slightly different version.

>>384835249
A and 7 or K and 2 in this case, am I right ?

>>384835135
Rewording of the same question

Four cards, drink on one side, age on another

Policeman tells you that "people drinking alcohol must be over 18"

Coffee Beer 16 43

Which ones to turn over to find those breaking the law? As few as possible


Easier now with real life context

>>384835449
A, K, and 7 is the answer.

>>384835584
Don't need to turn K over? The rule says nothing about consonants

>>384835658
You have to check that there isn't a vowel on the other side.

>>384835449
Only A, because the inverse is not strictly true. According to the rules only the vowel must have an even number on the other side, even numbers don't need to have vowels.

>>384815839
haha no way

>>384835801
Ah I see now it's not stated in that rule but I thought it must have a number on one side and a letter on the other side, if not then yeah

>>384835803
see
>>384835801
That version never states that there must be one number and letter on each card.

>>384835458
SO beer and 16
and the basic idea is
O N 4 1
I have to check if even number == vowel
and I have to check if N (can't translate that) ==odd number

If N == odd then 1 will be consonant (I tried)
and if 4 == vowel O will be even
r-right ?

>>384836235
You don't have to check O, since the man said
"Even numbers must have vowels on the other side"
he didn't say
"Vowels must have even number on the other side"
Like how the policeman doesn't say "Over 18s must be drinking alcohol"

Don't have to check 1 since it's not an even number and the man didn't say if they need vowel or consonant
Gotta check 4 to make sure it is a vowel on the other side, like the policeman has to check 16 to make they are not drinking alcohol

>>384815839
P(Detected | Loot) = .99
P(Detected | No Loot) = .01
P(Loot) = .001

P(Loot | Detected) = (.99 * .001) / (.99 * .001 + .01 * .999)
P(Loot | Detected) = .0902

.0902 * 100 = 9.02

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>>384836546
>"Even numbers must have vowels on the other side"
>he didn't say
>"Vowels must have even number on the other side
So you have to play with words like this
You don't care about 1 because it's not even
You don't care about O because it's vowel

That's pretty interesting

>>384835249
https://www.youtube.com/watch?v=t7NE7apn-PA

>>384837062
Yeah, he say
If A then B
Which is distinctly different from
If B then A

>>384836658
>99% of the time when it examines an enemy it correctly says whether or not they have loot

This is not the same as stating:
P(Detected | Loot) = .99
it is only stating that 99% of the time the detector is correct, which incorporates both true positives and true negatives rather than just true positives. All you know is that:
P(Loot)*P(Detected | Loot) + P(~Loot)*P(~Detected | ~Loot)= .99
but you don't know the numeric value of P(Detected | Loot)

https://www.youtube.com/watch?v=R13BD8qKeTg

https://en.wikipedia.org/wiki/Bayes%27_theorem

>>384837646
>99% of the time when it examines an enemy it correctly says whether or not they have loot
>but you don't know the numeric value of P(Detected | Loot)

Given loot, the probability of positive detection is .99. That is exactly what P(Detected | Loot) means.

>P(Loot)*P(Detected | Loot) + P(~Loot)*P(~Detected | ~Loot)= .99

Actually, that's .01098, AKA P(Detected).

>>384838293
>Given loot, the probability of positive detection is .99.
is not the same as
>99% of the time when it examines an enemy it correctly says whether or not they have loot

In the latter statement, which is from OP's post, it only refers to correctness of the detector in general, not the correctness of the detector given the condition that the enemy truly has loot. If I encounter an enemy that truly does not have loot and the detector says that the enemy does not have loot, then, the detector has correctly said "whether or not they have loot", so OP's statement, when read literally, incorporates true negatives as well.

>Actually, that's .01098, AKA P(Detected).
No, if we simplify,
P(Loot)*P(Detected | Loot) + P(~Loot)*P(~Detected | ~Loot)
P(Detected and Loot) + P(~Detected and ~Loot)
this isn't the same as P(Detected).

You are probably thinking of the expression
P(Detected and Loot) + P(Detected and ~Loot)
which does indeed equal
P(Detected)
but is not the same expression as what I stated

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>>384815839
>>384836658
>>384837646
>>384838293

>>384839101
I do understand Bayes' theorem and how it is relevant in the context of diagnostics and how it can be unintuitive. The main point I was trying to make is that the OP poorly worded the phrase that is supposed to define the "sensitivity".

I'm assuming his intention was to state that P(Detected | Loot) = .99, but he made a statement on the correctness of the detector as a whole instead:
>99% of the time when it examines an enemy it correctly says whether or not they have loot
The correctness of the detector incorporates both true positives and true negatives. Am I being pedantic? Yes, is it important to be pedantic when trying to understand probability problems to clarify intent> Yes.

>>384839798
OP here although I am about to go to bed

I meant for it to mean, when presented with a enemy that has loot, the detector says that they do 99% of the time. When presented with an enemy that doesn't have loot, it says that the don't 99% of the time. I thought was careful with the wording but maybe not enough