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FellowConspirator t1_ja83xfr wrote

Each time you roll the six-sided die, there's six possible outcomes: 1, 2, 3, 4, 5, 6. The probability of each one of those is 1/6 (16.66...%), and the total is 1 (100%). It doesn't change with each roll, because you aren't changing the die, or what you are doing. There's nothing connecting one roll to the next; they are completely independent.

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PM_ur_Rump t1_ja87fj5 wrote

I remember arguing with someone about this regarding seeing a plane crash at an airport and then getting on another plane. Others were talking about how they wouldn't get on their own flight after seeing that. This person said that it would make them feel safer, because "what are the odds that two planes crash on the same day?" I said they weren't getting on two planes though, they were getting on one, and the odds of one plane crashing didn't change when another crashed (of course assuming that all plane flights are equal).

The irrational mind sees a plane crash and goes "Fuck that, I'm not getting on a plane now, it's likely to crash."

The rational mind says "what are the odds of two planes crashing?"

The reality is somewhere in between. The chance was always there, but it didn't go up or down simply because this event occured.

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someone76543 t1_ja88ipg wrote

The odds probably went up slightly. Contaminated fuel, or bad weather, or technical problems with the ground systems, or terrorism, could cause multiple plane crashes. (Though I don't think that has ever happened accidentally... yet. Coordinated terrorist attacks have happened, such as 9/11).

Edit to add: There is also the risk of a design flaw on the aircraft. E.g. 737 Max. Or a consistent manufacturing flaw.

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PM_ur_Rump t1_ja8ad7h wrote

Or it could go down as everyone involved is now being more cautious.

I forget the exact scenario that inspired the conversation, but the person I was arguing with was definitely talking about the "odds" in the context of simple odds in the manner of "if a one in a million chance thing just happened, it's now probably closer to one in two million it happens again."

Odds only change when directly linked.

So if you are gambling on a dice roll and you bet that it will land on six, it's a one in six chance. If it does, and you bet on six again, the odds are still just one in six.

To change the odds, you would need to bet that it lands on six twice, because now you have linked the two rolls before they happen.

In the case of the plane crash, the odds of two planes crashing for independent reasons on the same day, involving the same airport, are much higher than a single plane crashing. Unfortunately for our hypothetical travellers, one plane already crashed, bringing the odds back down to the standard single-event odds.

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generous_cat_wyvern t1_ja8jk1c wrote

The issue when it applies to the real world is that you rarely get truly independent events. And also probability is based on assumed knowledge (or lack thereof), so gaining information changes probabilities.

An example is you have a shuffled deck of cards, and you're betting on the odds of the top card being an Ace of Hearts. The probability at this point is 1/52. If you happened to notice a flash of red as the dealer was shuffling, nothing about the deck changed, but now your odds are 1/26 because of additional knowledge.

If the first place crash revealed some information that wasn't available before, that can change the probability calculation, even if nothing else changed about the situation.

Also in a theoretical situation you accept the circumstances presented as fact. In the real world, those assumptions could be wrong, or someone could be flat out lying to you. Like if someone flipped a could 25 times and it landed on heads every time, mathematically you'd say you still have 50/50 for the next toss. But you are assuming that it is indeed a fair coin and not a weighted or double-headed coin. If you want into someone on the street taking bets, you have to factor in not just the odds at face value, but also the odds that they're cheating.

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nicktam2010 t1_jaa4hup wrote

Which is why they investigate aircraft crashes so thoroughly? So that a slight change in design, processes, procedures etc will further the body of knowledge about aircraft and the odds will decrease

It's the basis of all safety, I suppose.

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PM_ur_Rump t1_ja8sbsp wrote

Again, this was a discussion about theoretical simple odds. The real world isn't a coin flip, and like you pointed out the odds may be weighted in ways you don't know. But yeah, this was about him thinking that a die landing on six made it less likely to land on six again.

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generous_cat_wyvern t1_ja9n5ab wrote

Right, the OP was talking simple odds, but the thread shifted to talking about plane crashes I think we exit the realm where simple odds apply. It makes sense when we're talking about dice.

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PM_ur_Rump t1_ja9oemf wrote

I only brought it up because the guy I'm talking about was specifically talking about it in terms of simple odds, not arguing the fact that air travel is a very complex thing.

It was very much an application of the gambler's fallacy to a real world event, one that has extremely hard to quantify odds with countless variables to begin with.

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FellowConspirator t1_ja8ayep wrote

Here's a case where there might be a change in the odds. Usually, after a crash, there's a period of increased vigilance by ground crews to be on the look out for maintenance issues and speeding up checks of various systems. It's almost certainly safer to fly in the weeks following a high-profile crash.

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PM_ur_Rump t1_ja8c0jd wrote

Again, this discussion was very much about simple odds, not the complex odds of all the multiple factors. Dude even ironically used the words "gambler's fallacy" to describe what he thought I was doing by saying that one outcome does not effect the next.

In the real world, yes, there are connections between complex events like plane crashes, and the "odds" aren't static like dice.

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KLAPT0N t1_ja9j0wz wrote

Ok but what are the odds of 2 planes crashing from the same airport on the same day? That would would have a lower possibility right? If u saw a plane crash at the same airport u we’re taking off from hypothetically.

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PM_ur_Rump t1_ja9m8vr wrote

The odds of two planes crashing while flying in/out the same airport on the same day are far lower than the odds of a single plane crashing while flying in/out of that airport.

But.....

The odds of a plane crashing via that airport are not any lower after a plane has already crashed there, assuming in this hypothetical that plane crashes have specific odds and are not very complex events that are extremely hard to actually put "odds" on.

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SYLOH t1_ja8981f wrote

That's defective thinking as well.

Given that one plane crashed, it is much more likely that another plane of the same type will crash.

EG: a design mistake causes undue stress on a part, that part wears out faster that it should. That part breaks mid air and causes a plane crash. It is likely that the parts in all the similar planes has also been under stress, and might be breaking soon as well.

This is why the FAA tends to ground all planes of a certain kind until they figure out it wasn't the plane causing the issue.

See also the Boeing 737-800 MAX

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PM_ur_Rump t1_ja8b7cu wrote

See my other response.

But also think that there are all sorts of reasons planes crash, and all sorts of planes. A plane crashing at a large airport often does not significantly slow air traffic outside that directly impaired by the use of that runway or airport, depending on severity.

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SYLOH t1_ja8bwh3 wrote

And again, see the part about the Boeing 737-800 MAX.
Sometimes its a problem with the whole class of plane.
That's the most recent example I can name off the top of my head.
There are many many examples of this.

You can keep going to see sometimes how changes in process/certification lead to the crashes.
And sometimes that first crash is the sign those problems are starting to come home to roost.

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PM_ur_Rump t1_ja8cqu5 wrote

Yes, but that was not the conversation we were having.

And the grounding of whole fleets based on one event immediately after it has happened without reason to think it was a flaw in the design of the aircraft itself is not exactly common. When a plane overshoots the runway on landing due to pilot error, they don't ground entire fleets of that airframe.

Planes crashing is very complex thing and the "odds" are as well. It's not remotely static like dice.

That part was also part of the conversation I had with the guy in trying to explain the concept of odds to him.

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jjreason t1_ja8xo49 wrote

Unless the crashing plane damaged the departing plane & compromised its ability to function properly. I'll see myself out.

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Iminlesbian t1_ja9d89h wrote

But what are the chances that two different planes will crash at the same airport in one day?

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Aussie_Scientist t1_ja9i88s wrote

Very low. Once one plane has crashed they’re likely to close the airport. If there are no planes taking off or landing, the only way for a second crash to occur is a plane falling out of the sky directly at the airport.

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Iminlesbian t1_ja9idsr wrote

Nah but ignoring all that.

Like say it crashed but the after effects weren't taken into account.

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PM_ur_Rump t1_ja9e0fb wrote

Barring outside influences, and assuming the odds are static, like dice, exactly the same as one plane crashing there, once one already has.

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Iminlesbian t1_ja9i0us wrote

But not before right?

I'm not arguing, this just always kind of messes up my head.

Like the changes of me winning two lottery being the same because the chances of winning the lottery are the same for each ticket.

But how likely is it that someone who plays the lottery all of their life wins, and how likely is it that they win twice?

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PM_ur_Rump t1_ja9kw7z wrote

The odds that they win twice in a lifetime is much more unlikely than the odds they win once.

But after they won once, the odds of winning again are exactly the same as if they had never won.

Think of the dice example. There is a one in six chance of rolling a specific number. Rolling again, there is still a one in six chance of rolling that same number. The number of sides hasn't changed, the number you chose didn't magically disappear.

The odds only change if you bet that you will roll two in a row before the first roll, because you are now betting on both events before they happen, not on a single event happening. The events themselves have no influence on each other.

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Iminlesbian t1_ja9lehu wrote

Ah I get it, thanks a lot. The lottery chances "resetting" after the first win actually makes sense to me.

I think that's where my head gets confused. If I saw a plane crash I'd think of it as "well there's no chance of two of that thing happening today!" Rather than " it's still just as likely to happen today."

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PM_ur_Rump t1_ja9mk20 wrote

Glad I could help ya figure something out! It's definitely a bit counterintuitive at first, and I once had the same confusion. Cheers!

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SYLOH t1_jaav09w wrote

Do note. The guy seems to be talking about simple odds using real plane crashes for some reason.
Real world statistics do not work that way.

In the real world plane crashes are not independent events.
In the real world you knowledge of the odds of plane crashes is not complete.
A plane crash will cause the ground crew and flight crew to change their behavior, shifting the odds.
A plane crash is evidence that your assumptions on the safety of a given model of plane might be incorrect.

In the magical world of simple odds, safety audits and groundings wouldn't make a lick of sense. They do in the real world.

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breckenridgeback t1_ja8ol32 wrote

> There's nothing connecting one roll to the next; they are completely independent.

...under the assumption of a completely fair die. (An assumption you are usually making in a statistics class.)

In practice, though, the fairness of the die may be in doubt in many real-world scenarios.

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EspritFort t1_ja9if1k wrote

>>There's nothing connecting one roll to the next; they are completely independent.

> ...under the assumption of a completely fair die. (An assumption you are usually making in a statistics class.) > > > > In practice, though, the fairness of the die may be in doubt in many real-world scenarios.

You may have quoted the wrong passage there, because even without a fair die it still holds true. Whether the die is weighted towards a 6 or not, the individual rolls are still independent from each other, merely the probabilities of the outcomes are different.

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breckenridgeback t1_ja9jh3u wrote

> Whether the die is weighted towards a 6 or not, the individual rolls are still independent from each other, merely the probabilities of the outcomes are different.

The rolls are, but provided you have any uncertainty about the underlying probabilities, your beliefs about those rolls (and your expectations about the future rolls, which is the exact same thing) should be updating with each roll.

For a simple example, imagine I have two coins. One is loaded to always land heads, the other is fair. I pull one of the two from a box at random, and I do not know which I pulled. I want to estimate the probability of my next flip being heads. It's 75% in this case (50% to be loaded * 100% if it's loaded + 50% to be fair * 50% if it's fair).

I flip the coin, and it lands heads. This is evidence in favor of me having the biased coin. Specifically, I should update my probability that the coin is biased (using Bayes' rule) to:

P(loaded | heads) = P(loaded and heads) / P(heads) = 0.5 / 0.75 = 2/3.

Now I want to estimate the probability of the next flip. There is now a 2-in-3 chance (or more properly, that is my correct Bayesian estimation of that probability) that I am holding a biased coin, so the probability of the next flip being heads is 5/6 (it's 2/3 * 1 + 1/3 * 1/2 = 2/3 + 1/6 = 5/6). This is not equal to my original 3/4, even though the flips themselves are IID, because their underlying distribution depends on an unknown parameter about which I am gaining information.

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thunder_struck85 t1_ja9894k wrote

But if you roll a 6 ten times in a row, you could just have an unfair die. So in theory it's 1/6 always. But in the real world I would bet on it being a 6 the eleventh time 🤷

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