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"If there is a crash on 1 August, the chance that the next crash occurs one day later on 2 August is 1/365. But the chance the next crash is on 3 August is (364

"If there is a crash on 1 August, the chance that the next crash occurs one day later on 2 August is 1/365. But the chance the next crash is on 3 August is (364/365) x (1/365), because the next crash occurs on 3 August only if there is no crash on 2 August." Is this not the gambler's fallacy? Shouldn't the odds be unaffected by a previous crash?

darkxanthos 11y ago
In this case I would agree with you. I don't understand the reasoning for the last sentence at all.
- LeUsername 11y ago
  The focus is on being the next immediate crash. If you are asking whether there is a crash on 3 August, it is the unaffected odds of 1/365. But if you are asking whether the (first) next crash after 1 August is on 3 August, both the following must happen: a) there is no crash on 2 August b) there is a crash on 3 August The gambler fallacy would be "I have seen 9 days without crash, on the 10th day there is higher odds of crash". But you are not asking this, you are asking: "What is the chance that in the next 10 days, exactly first 9 days would be no-crash and on the 10th day there is a crash". EDIT: Also, another view: If you have seen 9 blacks in a row, there is an even chance 1/2 (roulette without zero) that the next will be black or red. Because in all sequences of length 10 starting with 9 blacks (this is given, you observed this), there is equal number of those with 9 consecutive blacks and a red and of those with 9 consecutive blacks and a black. This is gambler fallacy, believing that after repeated colour, you have higher chance of the other colour. Here, you are asking: how many of all sequences of length 10 have exactly 9 blacks and 1 red. And there are all kinds of sequences with 1 red in first 9 places, 2 reds, 3 reds, etc., so the odds of observing the 9 blacks in a row in the first place before asking about the 10th spin is lower, but it does not change the odds of the 10th spin itself.
  - darkxanthos 11y ago
    Super helpful! Thanks!
kcorbitt 11y ago
You're right that the probability that there is a crash on 3 August is unaffected by a potential crash on the 2 of August, but the chance that the crash on the 3 of August is the next crash (after the 1st of August) is affected.
- philh 11y ago
  Also, pedantically, a plane that crashes on the 2nd August isn't going to crash again on the 3rd. We can reduce the rate of crashes by taking planes out of the sky, and one way to do that is to crash them.
  - redcalx 11y ago
    Unless there are reserve planes that come immediately on-line to fill the gap (or the remaining planes do more fly time).
leni536 11y ago
In probability you have take attention to the very details. The statements "the next crash occurs on 3 August" and "there is a crash on 3 August" are not the same. Only the latter is independent from a crash on 2 August.

darkxanthos 11y ago

In this case I would agree with you. I don't understand the reasoning for the last sentence at all.

LeUsername 11y ago
The focus is on being the next immediate crash. If you are asking whether there is a crash on 3 August, it is the unaffected odds of 1/365. But if you are asking whether the (first) next crash after 1 August is on 3 August, both the following must happen: a) there is no crash on 2 August b) there is a crash on 3 August The gambler fallacy would be "I have seen 9 days without crash, on the 10th day there is higher odds of crash". But you are not asking this, you are asking: "What is the chance that in the next 10 days, exactly first 9 days would be no-crash and on the 10th day there is a crash". EDIT: Also, another view: If you have seen 9 blacks in a row, there is an even chance 1/2 (roulette without zero) that the next will be black or red. Because in all sequences of length 10 starting with 9 blacks (this is given, you observed this), there is equal number of those with 9 consecutive blacks and a red and of those with 9 consecutive blacks and a black. This is gambler fallacy, believing that after repeated colour, you have higher chance of the other colour. Here, you are asking: how many of all sequences of length 10 have exactly 9 blacks and 1 red. And there are all kinds of sequences with 1 red in first 9 places, 2 reds, 3 reds, etc., so the odds of observing the 9 blacks in a row in the first place before asking about the 10th spin is lower, but it does not change the odds of the 10th spin itself.
- darkxanthos 11y ago
  Super helpful! Thanks!

kcorbitt 11y ago

You're right that the probability that there is a crash on 3 August is unaffected by a potential crash on the 2 of August, but the chance that the crash on the 3 of August is the next crash (after the 1st of August) is affected.

philh 11y ago
Also, pedantically, a plane that crashes on the 2nd August isn't going to crash again on the 3rd. We can reduce the rate of crashes by taking planes out of the sky, and one way to do that is to crash them.
- redcalx 11y ago
  Unless there are reserve planes that come immediately on-line to fill the gap (or the remaining planes do more fly time).

leni536 11y ago

In probability you have take attention to the very details. The statements "the next crash occurs on 3 August" and "there is a crash on 3 August" are not the same. Only the latter is independent from a crash on 2 August.