Let's see if any of you can solve a math problem for 8th graders.
>>24620009
sorry to disappoint you anon. but im not doing your math.
The hypotenuse of the triangle is bent...
>>24620009
The math is not needed, just a good eye. You can see that the green and purple triangles are deformed just enough to allow for the inconsistency.
difference in slope
Shit I suck at math apparently
>>24620009
y=mx+b, nigga
>>24620119
they're both 13x8 though
I'm not getting trolled.
Einstein actually took notes on this problem, the shapes appear to fit perfectly but actually have a minuscule amount of space between them:
http://www.pitt.edu/~jdnorton/Goodies/Zurich_Notebook/solution.html
I'm bored, I'll take the b8.
Bait harder, OP.
>>24620009
>Where does the black area come from?
Straight outta Compton
>>24620285
C obviously
>>24620351
But if you choose an answer at random, the probability for choosing C is 25%, therefore it can't be C.
A and D are wrong because assuming either of them was correct, you would have a 2/4 chance (50%) so I'm going with B here? Still seems like a trick question though desu
>>24620458
Yes. It is a trick question.
>>24620458
Picking one at random would give you a 25% chance, hence either A or D; however that then changes the chances to give you 50% of getting the correct answer hence the answer is B.
>>24620458
>>24620496
The trick is that the queston is self-referential and any reasoning will end up in a loop. See Russel's antinomy/paradox for further reading.
Pic related has no trick to it, though.
>>24620285
1/4 chance, so 25%
A and D are 25% so 25x2= 50%
Thus B is correct
>>24620285
it's self-referential
if i remembered anything from probability & statistics class freshman year maybe i could formulate it and solve it
but fuck that
>>24620583
>>24620528
But the probabilty for choosing B (the supposedly right answer) at random is 25%, which means A und D are correct.
See>>24620579, >>24620590
>>24620579
Assuming you replace the coins and the tosses are independent, is it 11/20? If it's not you're going to need some conditional prob shit and desu I didn't pay enough attention in stats class to be able to remember that
Inb4 you have no coins left so it's 0
>>24620707
50/50 retard
either it is or isn't
50%
>>24620743
Yeah but you have 20 outcomes, 11 of which are heads. You don't know which coin was the last one so how can you say it's 50/50?
>>24620579
it does have a trick though, it's poorly worded
>you pick a coin at random, toss it, and record the result
>after ten tosses
is this ten tosses of the same coin, or ten iterations of the previous procedure?
it makes a difference
>>24620150
The graph is skewed. Cut up a right triangle in paper and you'll find the slopes to be different.
>>24620009
By deforming the green and purple triangles ever so slightly. It's an old trick.
>>24620707
nah this is wrong, remember that you have already succeeded 10 consecutive tails after a random selection. If you chose the unfair one then the probability of that is 100%, if you chose an unfair one then it is 1/1024. You have a 90% chance of choosing the fair ones so given 10240 trials you should get 10 consecutive tails on fair coins 9 times. Even in the unlikely case where it isn't the fake one that you have succeeded with, there is still a 50/50 chance so I'm going to throw a guess at 1 - 9/20480 or ~0.99956.
Tbh I cannot into probability anymore though so this is likely wrong.
>>24620150
look at the gradient of the green triangle and the blue triangle
Green triangle hypotenuse gradient = 3/5
Blue triangle hypotenuse gradient = 5/8
3/5 =/= 5/8 so when you switch them around you have a different triangle
The hypotenuse is different between the two triangles.
Notice the bright strip showing the difference between the two.
>>24620931
But each successive toss is independent of the previous one right? What you're saying is like if you got heads 10 times in a row, it's less likely that the next toss will be heads. Tbh my math only stretches to high school tier so I'm just confusing myself
>>24620579
It's always 50%
>>24621024
Each toss is independent. What I'm saying is that if you have managed to get 10 tails in a row, it's far more likely that you chose the fake coin rather than lucked out on a real coin. Choosing a real coin is 90% likely, but getting 10 tails is a 0.5^10 chance. So you end up with 0.9*0.5^10 = 0.0008789 chance of getting it on a real coin, but a 0.1*1 = 0.1 chance of getting it on a fake coin.
>>24620798
>responding to obvious bait
>>24620828
"After ten tosses" is more likely to refer to only the process of tossing the coin. But you're right, it's still open to interpretation, therefore ambiguous.
>>24620963
Actually, it's not a triangle at all, neither top nor bottom.
>>24620931
It's a little more complex desu. If I'm not mistaken it'S
s 10285/10330 or ~0.995644
>>24620931
the fact that you got 10 tails in a row shouldn't make a difference, though.
the probability of getting a tails next flip is going to be the probability of picking out a real coin * probability of tails + the probability of picking the fake coin * probability of tails
11/20
>>24621301
it does
you have to find the probability that your coin is fake, *given* that you've flipped 10 tails in a row
>>24621178
Fuck I guess I didn't read it properly, I assumed you were repeating the procedure every time but you're sticking with the same coin
Using P(A given B) = P(A and B)/P(B) the probability of having chosen the fake coin given 10 tails is the probability of having chosen the fake coin and getting 10 tails divided the the probability of getting 10 tails. I cba to work these out but if you calculate these and repeat for the probability of having chosen a normal coin, you should get the right answer
>>24620579
The same coin was thrown 10 times, as implied by "of that same coin".
Should it be a fair coin, the chance of 10 tails is .5^10 = 0.0009765625.
A both tails has a chance of 1.
The chance that a fair coin was thrown is (fair coin chance)x(no. of fair coins)/(double tails chance)x(no. of double tails)
= (0.0009765625 x 9) / (1 x1) = 0.0087890625
The chance a double tails was thrown is 1 - previous result = 0.9912109375
The answer is (fair coin probability) x (0.5) + (double tails probability) x (1) = 0.99560546875.
>>24620579
>choose a coin
>90% chance to be fair coin (50% tails probability)
>10% chance to be "both tails" coin (100% tails probability)
>90% chance to be 50% chance to be tails (fair coin)
>10% chance to be 100% chance to be tails ("both tails" coin)
>0.9 * 0.5 chance to get tails if you get a fair coin
>0.1 * 1.0 chance to get tails if you get "both tails" coin
>0.45 chance to get tails if you get a fair coin
>0.10 chance to get tails if you get "both tails" coin
>add both to get global chance of getting tails
>0.55 chance to get tails
>>24621301
How many tosses you have made and hoe they turned out doesn't really effect what the next toss will be. That is what you are saying and what most people will call ituitive. BUt think about it, after you have made a toss, you can determine probabilties for which coin you chose and based on that make predictions for the next toss. It's conditional probabilty. If you have made 10^100 tosses and all of them were tails, do still think the probability for the next one is 11/20? Because you know (almost) fr sure that you have the coin with two tails.
Assume you always toss the coin you chose at first. So we now have had tails ten times.
The probability for that event is P(10xT) = P(T/T) * P_T/T(10xT) + P(H/T) * P_H/T(10xT) = 1/10 * 1^10 + 9/10 * (1/2)^10 = 1033/10240
Further is: P(10xT) * P_10xT(T/T) = P(T/T) => P_10xT(T/T) = P(T/T) / P(10xT) = 1/10 / (1033/10240) = 1024/1033 This is the probabilty that you have the coin with two tails.
=> P_10xT(H/T) = 1- P_10xT(T/T) = 1 - 1024/1033 = 9/1033 Prob. for having a fair coin.
The probability for tails at the next toss is therefore P_10xT(T/T)*P_T/T(T) + P_10xT(H/T) * P_H/T(T) ? 1024/1033 + 1/2 * 9/1033 = 2057/2066 = ~0.995644
>>24620579
shit, after so many tails it gotta be a head.
but i dont know man, tail looks tough tho, so many times tail won. hmm. my guess is its 0.55 tail
a portion is taken out tbuuj famillia
>>24620579
he probability of getting n tails is
1/10 + 9/10 * (1/2)^n
Let A be the event where you get 11 tails and B the event where you get 10 tails. We then have P(A|B) = P(A and B) / P(B), so you have a probability of 2057/2066 ~ 99.56% to get tails.
>>24620009
The area of a 8x13 triangle is 8*13/2=52. So fig 1 is not using the area completely, and fig 2 is overfilling it. You can't see that though because the difference with the real area is less than 1%.
>>24622515
That's brilliant, sensei. Have a (You), you deserve it.
