EPTThis is just the same as the 'gambler's fallacy' in roulette, even if red comes up a hundred times in a row it's still just as likely to come up red the next time.
Coins tosses - Page 2
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jello_biafra
United Kingdom6638 Posts
This is just the same as the 'gambler's fallacy' in roulette, even if red comes up a hundred times in a row it's still just as likely to come up red the next time. | ||
Chill
Calgary25987 Posts
The entire thread has explained this. The fact that either coin could be H gives you two chances to be right, whereas there is only one chance to be wrong (HH). The other chance of being wrong (TT) was eliminated by the statement "One coin is heads". 2 / 4 now becomes 2 / 3. | ||
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Sea_Food
Finland1612 Posts
EDIT: Explain how it is wrong? | ||
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Shifft
Canada1085 Posts
There are two balls in a bag, one green and one red. You pick one at random. So at the time that you picked there is pretty clearly a 50% chance that you pick the red ball. Now, without looking at the ball you picked, your friend tells you that the green ball is still in the bag. Due to this additional information you now know that the chances of the ball you picked being red are 100%, even though at the time you picked the chance was only 50%. The coin examples function basically the same way, but there are more possibilities. | ||
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Hesmyrr
Canada5776 Posts
T T 25,0000 T H 25,0000 H T 25,0000 H H 25,0000 Above is the result you get from tossing two coins 1 000 000 times. Now you LITERALLY THROW AWAY THE 25,0000 results you got (TT) since it does not meet the specified parameter (at least one coin has flipped head). Coin 1 / Coin 2 T H 25,0000 H T 25,0000 H H 25,0000 About 50,000 times one of the coin flipped heads and another flipped tails. And about 25,000 times both of the coins flipped head. Since we are not talking about how coin 1 or coin 2 flipped but how the coin that is not heads (it can be coin 1 OR coin 2) flipped, 500000/750000 = 2/3. Try it yourself. Flip two coins 100 times, and you will understand what we mean. | ||
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Blisse
Canada3710 Posts
You should take any intro to probability course at any level high school+. It's actually pretty interesting and should run you through the basics. A lot of people struggle through it since it really isn't intuitive unless you're willing to open your mind a bit to learn and accept this slightly crazier reality. Your counterexample fictional scenario is wrong, though I'm not sure what you're talking about still. The possible outcomes are either: HT HH TH HH In other words, it doesn't matter which coin you throw first, only the results of the fair coin matter. And the fair coin is 50/50 for H/T. Not 33. | ||
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Hesmyrr
Canada5776 Posts
On July 16 2011 03:11 Blisse wrote: Your fictional scenario is wrong, though I'm not sure what you're talking about still. The possible outcomes are either: HT HH TH HH  | ||
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Monoxide
Canada1190 Posts
On July 16 2011 02:55 Tatum26 wrote: I think i understand the mixup. if you have TH and HT as two separate options, shouldn't there also be two HH's? as your double-headed coin could land on either head. Nope. There is only 2 coins. HH means the first coin was a head and second was also a head. There can't be another scenario where there is another HH. | ||
]343[
United States10328 Posts
You have two fair coins, each with a heads and a tails side. You aren't allowed to flip 2 tails: that is, whenever you flip two tails, flip both again. The probability you will get 2 heads now is indeed 1/3. | ||
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OpticalShot
Canada6330 Posts
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Hesmyrr
Canada5776 Posts
On July 16 2011 03:12 ]343[ wrote: You have two fair coins, each with a heads and a tails side. You aren't allowed to flip 2 tails: that is, whenever you flip two tails, flip both again. The probability you will get 2 heads now is indeed 1/3. This is best and simplest way of describing it. Btw, is there any other famous mathematical mindfucks? I am curious  | ||
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Jumbled
1543 Posts
On July 16 2011 02:44 Sea_Food wrote: Then why do all the outcomes in the orriginal story have equal probabilities? Because it's a different problem. In the first example, you have four outcomes with equal probability, one of which is excluded due to extra information you receive. In the second example, there are only three possible outcomes in the first place, and one of those is more likely than the others. | ||
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monkxly
Canada241 Posts
You're on a gameshow, and there are three doors Behind one of the doors there is a prize You choose a door, and the game show host opens one of the other doors and shows there is nothing on the other side. You can now switch doors, should you? It's the same problem as the op in concept | ||
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Sea_Food
Finland1612 Posts
On July 16 2011 03:09 Hesmyrr wrote: Coin 1 \ Coin 2 (Adding the title because it's important, first result refers to what coin 1 flipped as and second result refers to what coin 2 flipped as) T T 25,0000 T H 25,0000 H T 25,0000 H H 25,0000 Above is the result you get from tossing two coins 1 000 000 times. Now you LITERALLY THROW AWAY THE 25,0000 results you got (TT) since it does not meet the specified parameter (at least one coin has flipped head). No I dont, because if he tosses coins that many times, he will throw TT some times, in which case he cannot tell me one of the coins landed H. | ||
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Impervious
Canada4211 Posts
On July 16 2011 03:14 Hesmyrr wrote: This is best and simplest way of describing it. Btw, is there any other famous mathematical mindfucks? I am curious e^(i(pi)) = -1 | ||
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Vertig0
United States196 Posts
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Hesmyrr
Canada5776 Posts
On July 16 2011 03:16 monkxly wrote: yep, I have one that's probably more famous You're on a gameshow, and there are three doors Behind one of the doors there is a prize You choose a door, and the game show host opens one of the other doors and shows there is nothing on the other side. You can now switch doors, should you? It's the same problem as the op in concept Going straight with my intuition here, I should because now it is 1/2 instead of 1/3. Right? Actually yeah, that seems slightly more flimsy than the OP's example :O (or at least it feels more like it) | ||
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Essbee
Canada2371 Posts
What does "i" stands for? btw, I understood the OP with what ]343[ wrote, thanks. | ||
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Impervious
Canada4211 Posts
On July 16 2011 03:20 Hesmyrr wrote: Going straight with my intuition here, I should because now it is 1/2 instead of 1/3. Right? Actually yeah, that seems slightly more flimsy than the OP's example :O (or at least it feels more like it) 2/3 actually. Why? | ||
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Impervious
Canada4211 Posts
On July 16 2011 03:21 Essbee wrote: What does "i" stands for? btw, I understood the OP with what ]343[ wrote, thanks. i = sqrt(-1) | ||
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