Is there more stuff like this?

Smart

Exclusively on probability or any kind of unintuitive result?

...

he didn't say which coin is guaranteed to be heads

2/3?

Any intro to probability course/book
youtu.be/SmFwFdESMHI

at the risk of being retarded: 50%

[math] {1 \over 2} \times {1 \over 2} = {1 \over 4} [/math] where the third box being negligible, having two balls on each box (if the first ball was returned to the box), on two boxes.

If the gold ball was removed from the box, the answer will be [math] 1 \over 2 [/math]

It doesn't matter if you flip the double headed coin first or second. You are still only flipping 1 coin

if you have a gold ball, there is a 2/3 chance that it was from the first box. Therefore, there is a 2/3 chance that the next ball will be gold

the coins are normal, there is no double headed coin. with one coin being heads there are three possibilities: heads/heads, heads/tails, tails/heads

but it can't be from the third box so isnt it a 1/2 chance it's from the first box??

I don't see your reasoning. 1/3 gold balls are in the second box. 2/3 are in the first.

Ohhh but you're picking between boxes not balls

2/3

Whether the ball is gold or not entirely depends on which box you've picked. There's a 2/3 chance that you've picked the box with 2 gold balls, therefore there's a 2/3 chance that the next ball will be gold.

But there's only a 1/2 chance that you picked the box with two gold balls because you picked a gold ball and there's only two boxes that have gold balls

this is the goat thing all over again
I have to review my stats, I aced intro stats man, I guess I just forgot how Bayes theorem works

pick box 1: pick gold ball
pick box 1: pick gold ball
pick box 2: pick gold ball
pick box 2: pick silver ball (ignore)
pick box 3: pick silver ball (ignore)
pick box 3: pick silver ball (ignore)

there are two boxes with gold balls but there are three outcomes

picking a ball at random an arbitrary amount of times from the three boxes, 1/2 times you will pick a gold ball. how many times do you think the gold ball will come from the box with 2 golds as opposed to the box with 1?

Possible scenario’s when drawing 2 balls from one box:
Gold1 – Gold2
Gold2 – Gold1
Gold1 – Silver2
Silver2 – Gold1
Silver1 – Silver2
Silver2 – Silver1

The first ball was Gold so for the second ball you are left with three options, two of which are Gold.

So 2/3

No, one of them is effectively a double headed coin. Meaning flipping or not flipping the double headed coin does not change the outcome. The resulting probabilities is the same as flipping a single coin

wrong.
there 4 different outcomes.
heads(chance coin)/heads(double heads coin), heads(double heads coin)/heads(chance coin), heads/tails, tails/heads

>HURR DURR
math.stackexchange.com/questions/991060/flip-two-coins-if-at-least-one-is-heads-what-is-the-probability-of-both-being

>at least one is heads
is not the same as
>one is guaranteed heads

now that's some mental gymnastics. it's perfectly valid to interpret "flip TWO coins" and "one is guaranteed heads" as "at least one is heads"

>it's perfectly valid to interpret "flip TWO coins" and "one is guaranteed heads" as "at least one is heads"
No, it’s not.

They both have different probability space
>guaranteed heads
This means, guaranteed IN ADVANCE. Making it a double headed coin, which means you can remove it from the equation altogether. As said

Probability space:
H
T

>at least one is heads
This means, heads AFTER the flip

Probability space:
H1-H2
H1-T2
T1-H2
T1-T2
When one of the coins is heads you are left with 3(!) options for the second coin (only T1-T2 is eliminated) Of those three options there are two in which the other coin is also heads.

if that's what the original user meant it'd just be a silly word trick to get (You)s. kys

the other user just worded it wrong

It doesn't matter what original user meant. The answer to the question he posted is clearly 50%. To presume another question instead just because you think it is a better question is retarded.

no, fuck off. it says flip two coins. it doesn't say that one is a special double headed coin. it's a stretch to make the assumptions you're making.

it's ambiguous at best because of wording and the impreciseness of human language

dude...how can we really know anything bro? fuuuckk...

yes it says 2 coins, but one is guaranteed heads. That means no matter how you flip it, or even if you flip it, you know it will land heads. If you want to think about it differently: for one of the coins, you are going to manually turn it over if it lands tails, forcing it heads no matter what.

That is what guaranteed means. It doesn't matter how you guarantee it, but one of the coins has a 100% chance of heads.

Why do you assume a two-headed coin and not that, for the purposes of the riddle, the one who tells you the riddle knows the outcome of the coin flip in advance?

I doesn't matter how the heads is guaranteed, the outcome is the same

No it isn't. You're guaranteed one heads. You don't know which one.

So you don't know which coin is two-headed, just that one is two-headed. Literally still the same outcome. If you guarantee one of the two is heads then you are only flipping 1 coin. It doesn't matter when you "spend" the head you are guaranteed.

There is no two-headed coin. You're just talking to a psychic who guarantees you one heads. That's literally 100% the same as "at least one coin is heads".

Just like the monty hall problem, you can ACTUALLY TRY IT AT HOME. in the absence of a two headed coin, just mark one of them with a sharpie to be interpreted as heads no matter how you flip it (effectively you don't have to flip it)

Actually, just discard trials where both coins landed tails. That is the probability.

it is just as valid to assume that one is guaranteed to be heads because it is a trick coin as it is to assume that "luck magic" simply throws out the results where two tails would have been thrown.

>just get rid of the experiments that don't prove my hypotheses and you will see I was right all along.

How do you make fifty-five cents with two coins if a single one can't be a nickel?

get change back

what are you talking about?
there are only two coins so they mean the same thing
one has to be heads either way, the other one is up to chance

you worded this one wrong on purpose, didn't you?

2/5?

So while holding one gold ball in your hand, you know that there are 2 boxes containing gold balls. The odds of picking up another gold ball are the same as choosing between 2 boxes; one containing a silver ball and a gold ball, and the other one containing 2 gold balls (50%). This is how my brain interprets the scenario without any further thinking. Slap me back into reality if you think I'm wrong

WRONG
Bayes theorem is back at it again
I don't understand it either
It's like when you go to choose the next ball the probabilities have changed or some shit baka

Really convincing baka

I looked it up though
"Bertrand box"

It's 2/3. Once again, CompSci proves to be superior.
jsfiddle.net/mcec9w4q/6/

The key here is SAME BOX
You have reached in and picked a gold coin, this is a given

The odds of having picked it from the box with 2 silver coins? 0%, no gold coins there

The odds of having picked it from the box with 1 gold and 1 silver? 33%, because 1/3rd of the total gold coins are there

The odds of having picked it from the box with 2 gold coins? 66%, because 2/3rds of the total gold coins are there

So let's focus on the latter two:

In the 33% chance that you picked it from the box with 1 silver and 1 gold, the next one you pick will certainly be silver

In the 66% chance that you picked it from the box with 2 gold coins, the next one will certainly be gold

Ergo, given the conditions, 66% of the time you will find another gold one.

K my question: how do you know when to stop counting boxes and start counting coins? What tips you off?

I mean, you never count the boxes. You count the coins to count the probability that you've picked a coin out of one box or another. The relevant calculation is "what are the odds that I picked a gold coin out of this box as opposed to that box" (to which the answer is 2/3 in the 2gold one because 2/3 of the gold coins are there)

yeah man that's not intuitive to me but I finally understand
it's just so weird how you can basically ignore the boxes completely

>Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?

A) Yes
B) No
C) Cannot be determined
>Imagine that the U.S. Department of Transportation has found that a particular German car is eight times more likely than a typical family car to kill occupants of another car in a crash. The federal government is considering resticting sale and use of this German car. Please answer the following two questions: Do you think sales of the German car should be banned in the U.S.? Do you think the German car should be banned from being driven on American streets?

>Imagine that XYZ viral syndrome is a serious condition that affects one person in 1,000. Imagine also that the test to diagnose the disease always indicates correctly that a person who has the XYZ virus actually has it. Finally, suppose that this test occasionally misidentifies a healthy individual as having XYZ. The test has a false-positive rate of 5 percent, meaning that the test wrongly indicates that the XYZ virus is present in 5 percent of the cases where the person does not have the virus.
>Next we choose a person at random and administer the test, and the person tests positive for XYZ syndrome. Assuming we know nothing else about that individual's medical history, what is the probability (expressed as a percentage ranging from zero to 100) that the individual really has XYZ?

(continued)

>As seen in the pic, four cards are sitting on a table. Each card has a letter on one side and a number on the other. Two cards are letter-side up, and two of the cards are number-side up. The rule to be tested is this: for these four cards, if a card has a vowel on its letter side, it has an even number on its number side. Your task is to decide which card or cards must be turned over to find out whether the rule is true or false. Indicate which cards must be turned over.

Source: scientificamerican.com/article/rational-and-irrational-thought-the-thinking-that-iq-tests-miss/

>don't understand

Not that hard, see stage #1: 3 ways to have picked the first gold
stage #2: Next ball, 1 silver, 2 golds

yes, regardless of whether anne married or not.
no idea/no idea
very low, 2% if my mental math is right

you need to check the A and the 5.

it doesn't need to refer to one specific coin. the two coins could just as well be normal coins and to satisfy the guarantee of one being heads you could for example have re-rolls if both lands on tails

1. yes
2. seems to have more to do with politics than to be a strictly yes/no question
3. 1/(1 + .05*999) = ~2.0%
4. the cards with A and 8 on them

>4. the cards with A and 8 on them
damnit fml

No it is not, it is the same as one is guaranteed heads, only one coin is actually being flipped. If the psychic knows, with 100% certainty that one coin will land heads, then that coin isn't actually being flipped, because flipping it doesn't influence the probability of the outcome in any way.

Think about it from a simulation point of view, you wrote a simple program that flips too coins, then chooses one at random and forces the result heads (before looking at the result of either coin). Then it counts how many times both are heads and how many times at least 1 is tails. The result will be 50% because one and only one coin is actually being flipped.

Even without a 2 headed coin, it is effectively the same no matter how you guarantee one of the coins lands heads.

stupid normie
you can't even imagine anything other than your first assumption

Do a couple of flips yourself. It would be trivial to get a computer to do it for you if you want a few million flips instead and know even basic programming.

No, that is "at least 1 heads" not "one of the coins is guaranteed heads." The difference is you are only guaranteeing one of the coins is heads IF neither are heads. That only happens 25% of the time. For half of that coin's flips, it is landing tails when it should be landing heads, but you don't care because the other, non-guaranteed coin is landing heads for it.

To guarantee one of coins always lands heads, its probability of tails must be 0. You can't count it half of the time.

...

kill yourself sperglord

it says FLIP TWO COINS

not one coin

it only says that you're guaranteed that one coin is heads, it doesn't say which coin

m8

If the psychic knows that at least one coin is heads

Then the psychic can guarantee you one heads

They're synonymous

Correct, it doesn't matter if you flip the coin that is guaranteed heads first or second, you still have a 100% chance of one being heads, and a 50% chance of the other being heads. 1 * .5 = .5, an overall 50% chance of both being heads.

The psychic doesn't just know at least one is heads, the psychic knows which coin will land heads. That is the difference. "one [of the coins] is guaranteed to be heads", not "is guaranteed one of the coins to be heads."

>The psychic doesn't just know at least one is heads, the psychic knows which coin will land heads.
Sez you. But that's a superfluous assumption.
>"one [of the coins] is guaranteed to be heads", not "is guaranteed one of the coins to be heads."
No, because the latter is not a grammatically correct sentence, and if it had been it would resemble the former.

They could be both double headed coins

>This means, guaranteed IN ADVANCE. Making it a double headed coin, which means you can remove it from the equation altogether.
see

you're being retarded on purpose. here's your (You)

It us only not grammatically correct because I wanted the use the same words from the original question. As stated, it guarantees one of the coins to be heads, and will always be heads. The question you would rather answer is that one of the outcomes is guaranteed heads. Wording that question as close to as originally stated would be:

If you flip two coins and one of the results is guaranteed to be heads, what's the chance that both will be heads?

But because the only noun before "one" is the coins, the one must refer to a coin, and guaranteeing a coin to be heads reduces the probability of it ever landing on tails to 0.

These are two different questions, and the former is the more correct interpretation of the original in the thread. Your question is the more common, and arguably the better math question, but it was not the question asked in the thread. Your bias towards it, either because of your experience with it or whatever, is causing you to misinterpret the question.

I am not misinterpreting shit, and in fact you have to have some sort of autism to fail to realise that "coin" stands for "the result of a coin flip" in this context. In fact, if we interpret the question as you do, then isn't it also asking for the odds that both coins are double-headed? Which is impossible to know.

ONE COIN is guaranteed to be heads.
not "It cannot be the case that both coins come up tails"

Both statements are equivalent.

No, I'm saying it was phrased
No one here was ever disputing the logic behind the two child family problem, mostly because we never got that far.

3/4 right?
first coin second
heads (50%)-> (heads 25%- tails 25%)*25% of total
tails (50%)-> heads (50%)
25+50=75

nevermind i fucked up sorry guys

so it woudl be 1/4 then?

1/3 because one is guaranteed heads so you can't have tails-tails

OKAY LOOK HERE FUCK BOYS

>One of the coins is double sided (heads)
T - H
H - H
T - H
H - H

Chance of two heads: 1/2

>One of the coins is guarantied to be heads. No double sided coin.

T - T (Ignored)
T - H
H - T
H - H

Chance of two heads: 1/3

THERE. PROBLEM RESOLVED.

this

Are you an idiot?
NOT(F AND F) is T.
NOT(T AND T) is F.

TFFF IS NOT EQUAL TO FTTT.

Why count the coins/balls instead of the boxes? You cannot see into the boxes, so you are selecting from a set of boxes rather than coins/balls. That is to say, you're selecting boxes with contents associated with them, not selecting the contents and checking which box it's associated with. Hopefully I got the distinction across correctly.

Actually, nevermind. Just figured it out, am retarded.

Youre pulling from the same box user. 1/2