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Reminds me of this part from Taleb: "Assume that a coin is fair, i.e., has an equal probability of coming up heads or tails when flipped. I flip it ninety-nine

by twien 7y ago

Reminds me of this part from Taleb: "Assume that a coin is fair, i.e., has an equal probability of coming up heads or tails when flipped. I flip it ninety-nine times and get heads each time. What are the odds of my getting tails on my next throw? 2 Dr. John refers to the question as trivial and gives the mathematically correct answer of one half. Fat Tony calls Dr. John a sucker and says, “no more than 1 percent, of course … the coin gotta be loaded.”" The point being, what are the odds of getting an artifact of statistics precisely when management is harrassing employees to get rid of them from payroll?

strictfp 7y ago
The mind-twisting part of statistics is that Fat Tony is partially right. Because although each independent throw has the probability of one half, the total resulting series is very unlikely. So you could simultaneously be at awe of the incredible improbability of throwing another heads while proclaiming meh over the 50% chance of the last throw. It's all a matter of perspective.
- Gibbon1 7y ago
  Tony knows the chance of head 99 times in a row is enormously smaller than the chance he's being played for a sucker.
- moring 7y ago
  The point is this: "Assume that a coin is fair" ... "the coin gotta be loaded" In the example, Fat Tony is wrong because he contradicts the initial assumption. However, the example is unrealistic because, initially, you don't know if the coin is fair or loaded. You just flip it, see 99 heads and then conclude, with probability very close to 1, that the coin is loaded. (You could still be wrong, but likely aren't). So in a realistic scenario, Fat Tony would be right, except that the scenario was intentionally set up to be unrealistic. (edit: typo)
RivieraKid 7y ago
Well the answer of 50% is not just mathematically correct, it's simply correct, because the question said we must assume that the coin is fair. If this was a real life situation, we would assume a reasonable prior for the probability of heads, perhaps with a spike around 0.5 and a small value everywhere else. The posterior would be centered near 1.
FreeFull 7y ago
The interesting thing is that you can't bias a real coin (unless it's allowed to bounce around after falling). As long as you catch the coin after flipping, you're going to get 50/50 chances, no matter how the coin is weighted. https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf

by twien 7y ago

strictfp 7y ago

The mind-twisting part of statistics is that Fat Tony is partially right. Because although each independent throw has the probability of one half, the total resulting series is very unlikely. So you could simultaneously be at awe of the incredible improbability of throwing another heads while proclaiming meh over the 50% chance of the last throw. It's all a matter of perspective.

Gibbon1 7y ago
Tony knows the chance of head 99 times in a row is enormously smaller than the chance he's being played for a sucker.
moring 7y ago
The point is this: "Assume that a coin is fair" ... "the coin gotta be loaded" In the example, Fat Tony is wrong because he contradicts the initial assumption. However, the example is unrealistic because, initially, you don't know if the coin is fair or loaded. You just flip it, see 99 heads and then conclude, with probability very close to 1, that the coin is loaded. (You could still be wrong, but likely aren't). So in a realistic scenario, Fat Tony would be right, except that the scenario was intentionally set up to be unrealistic. (edit: typo)

RivieraKid 7y ago

Well the answer of 50% is not just mathematically correct, it's simply correct, because the question said we must assume that the coin is fair. If this was a real life situation, we would assume a reasonable prior for the probability of heads, perhaps with a spike around 0.5 and a small value everywhere else. The posterior would be centered near 1.

FreeFull 7y ago

The interesting thing is that you can't bias a real coin (unless it's allowed to bounce around after falling). As long as you catch the coin after flipping, you're going to get 50/50 chances, no matter how the coin is weighted. https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf