Odds, probabilities and "what's the chances of that?"

[glenrobbo]

TwigtheWonderkid said:

If you read thru the thread, he went on to say 100 sheep, 100 fields, one in each.

Ah. I missed that, sorry.

Oh well, in that case, "Sorry, but Ah'm oot".

[otolith]

TwigtheWonderkid said:

OK, if all the fields are the same, then sheep 1 could have died in any field . The chances of sheep 2 and 3 both dying in the same field as sheep 1 is ten thousand to one. (100 x 100).

It's quite possible, but unlikely. My guess is something environmental in that field is killing them.

If you insure 100 drivers, and there are three at fault accidents, what is the probability that it's the same driver...

[TwigtheWonderkid]

otolith said:

If you insure 100 drivers, and there are three at fault accidents, what is the probability that it's the same driver...

Again, more info needed. If you insure 99 55y/o women with Micras, and an 18y/o bloke with a Subaru WRX, I'd say pretty high!

Even if you insure 100 people with the same profile, the one who has the first accident is more likely to have the next one. Because you need to factor in the possibility they are a dangerous driver, and it wasn't just a one off error. If the same person has the first 2 accidents, the chances that the problem is them get even higher, so they're even more likely to be involved in accident 3.

[otolith]

TwigtheWonderkid said:

otolith said:

If you insure 100 drivers, and there are three at fault accidents, what is the probability that it's the same driver...

Again, more info needed. If you insure 99 55y/o women with Micras, and an 18y/o bloke with a Subaru WRX, I'd say pretty high!

Even if you insure 100 people with the same profile, the one who has the first accident is more likely to have the next one. Because you need to factor in the possibility they are a dangerous driver, and it wasn't just a one off error. If the same person has the first 2 accidents, the chances that the problem is them get even higher, so they're even more likely to be involved in accident 3.

Exactly my point.

What you answered was "what would the probability be if the incidence of sheep death were random and unbiased" - which is a useful calculation if you are trying to determine whether what happened was likely to be just random chance or something more sinister, but is less useful if you are trying to project the probability of clustering of sheep deaths in order to - I don't know, predict how much room you need in each field for burying sheep carcasses!

[otolith]

(you might have a priori knowledge of sheep and fields in general which would give you a better model - diseases are infectious, fields are at risk of flooding or not at risk of flooding, etc)

[TwigtheWonderkid]

otolith said:

TwigtheWonderkid said:

otolith said:

If you insure 100 drivers, and there are three at fault accidents, what is the probability that it's the same driver...

Again, more info needed. If you insure 99 55y/o women with Micras, and an 18y/o bloke with a Subaru WRX, I'd say pretty high!

Even if you insure 100 people with the same profile, the one who has the first accident is more likely to have the next one. Because you need to factor in the possibility they are a dangerous driver, and it wasn't just a one off error. If the same person has the first 2 accidents, the chances that the problem is them get even higher, so they're even more likely to be involved in accident 3.

Exactly my point.

What you answered was "what would the probability be if the incidence of sheep death were random and unbiased" - which is a useful calculation if you are trying to determine whether what happened was likely to be just random chance or something more sinister, but is less useful if you are trying to project the probability of clustering of sheep deaths in order to - I don't know, predict how much room you need in each field for burying sheep carcasses!

If you read my post on P1, I did make the point that if true, I'd go for an environmental cause over a 10K/1 coincidence.

[otolith]

TwigtheWonderkid said:

If you read my post on P1, I did make the point that if true, I'd go for an environmental cause over a 10K/1 coincidence.

Not just environmental cause, though. The probability model might be completely wrong even if all the fields and sheep are identical if in general deaths tend to be clustered (because for instance the most common cause of deaths is an outbreak of something communicable in the field).

[Lily the Pink]

To get back to the original question ...

Louis Balfour said:

A sheep farmer owns 100 fields.

He has owned the fields for 17 years.

In 17 years he has had three sheep die.

All sheep died in the same field.

What are the chances of that happening?

The answer is "vanishingly small".

I don't believe for one moment that any sheep farmer owns 100 fields.

[Ayahuasca]

TwigtheWonderkid said:

Esceptico said:

The probability is likely much higher than you think. By coincidence read the linked article yesterday. Mathematician gave example: if you throw 100 grains of rice into the air in room with 400 tiles are you likely to find a tile with 5 grains of rice on it? “Common sense” says no but if you do the experiment it is not unusual.

https://www.theguardian.com/commentisfree/2020/oct...

In general people are not very good with estimating probability (beyond very simple examples).

This is a very simple example, and can be answered with basic maths. It's 10,000/1.

Wrong. The probability is much higher than that. Rice has low mass and air resistance will slow it considerable. Most grains will fall on the few tiles surrounding the thrower, and most tiles will have zero grains on them, but some will have a lot.

[Jinx]

Lily the Pink said:

The answer is "vanishingly small".

I don't believe for one moment that any sheep farmer owns 100 fields.

They are very small and only large enough for one sheep.......

[Mammasaid]

Lily the Pink said:

I don't believe for one moment that any sheep farmer owns 100 fields.

Unfortunately, you're wrong there, I know 3 in my local vicinity, i.e with 5 miles, who farm > 100 fields. We have 50 acres, 150 sheep and 11 fields and we're small fry.

[TwigtheWonderkid]

Ayahuasca said:

TwigtheWonderkid said:

Esceptico said:

The probability is likely much higher than you think. By coincidence read the linked article yesterday. Mathematician gave example: if you throw 100 grains of rice into the air in room with 400 tiles are you likely to find a tile with 5 grains of rice on it? “Common sense” says no but if you do the experiment it is not unusual.

https://www.theguardian.com/commentisfree/2020/oct...

In general people are not very good with estimating probability (beyond very simple examples).

This is a very simple example, and can be answered with basic maths. It's 10,000/1.

Wrong. The probability is much higher than that. Rice has low mass and air resistance will slow it considerable. Most grains will fall on the few tiles surrounding the thrower, and most tiles will have zero grains on them, but some will have a lot.

I'm not talking about rice, I'm talking about the 100 identical sheep in 100 identical fields.

[coppernorks]

The odds of a Scorsese film with a decent female character ?

[Ayahuasca]

TwigtheWonderkid said:

Ayahuasca said:

TwigtheWonderkid said:

Esceptico said:

The probability is likely much higher than you think. By coincidence read the linked article yesterday. Mathematician gave example: if you throw 100 grains of rice into the air in room with 400 tiles are you likely to find a tile with 5 grains of rice on it? “Common sense” says no but if you do the experiment it is not unusual.

https://www.theguardian.com/commentisfree/2020/oct...

In general people are not very good with estimating probability (beyond very simple examples).

This is a very simple example, and can be answered with basic maths. It's 10,000/1.

Wrong. The probability is much higher than that. Rice has low mass and air resistance will slow it considerable. Most grains will fall on the few tiles surrounding the thrower, and most tiles will have zero grains on them, but some will have a lot.

I'm not talking about rice, I'm talking about the 100 identical sheep in 100 identical fields.

What are the chances of that?

[talksthetorque]

Is it the nearest field to the farmhouse kitchen?

[Nimby]

otolith said:

TwigtheWonderkid said:

OK, if all the fields are the same, then sheep 1 could have died in any field . The chances of sheep 2 and 3 both dying in the same field as sheep 1 is ten thousand to one. (100 x 100).

It's quite possible, but unlikely. My guess is something environmental in that field is killing them.

If you insure 100 drivers, and there are three at fault accidents, what is the probability that it's the same driver...

If your car was damaged by a meteorite from Mars, would your premiums increase as "it was more likely to happen again"?

[NoisyGriff]

Lily the Pink said:

Esceptico said:

Mathematician gave example: if you throw 100 grains of rice into the air in room with 400 tiles are you likely to find a tile with 5 grains of rice on it?
...
In general people are not very good with estimating probability (beyond very simple examples).

It is similarly counter-intuitive that in a class of 25 pupils, it is more likely that two pupils share a birthday than it is that none of them do.

Any chance you could run me through the maths behind this? I'm sure you're right, but I can't quite fathom it myself.

[Dr Jekyll]

NoisyGriff said:

Lily the Pink said:

Esceptico said:

Mathematician gave example: if you throw 100 grains of rice into the air in room with 400 tiles are you likely to find a tile with 5 grains of rice on it?
...
In general people are not very good with estimating probability (beyond very simple examples).

It is similarly counter-intuitive that in a class of 25 pupils, it is more likely that two pupils share a birthday than it is that none of them do.

Any chance you could run me through the maths behind this? I'm sure you're right, but I can't quite fathom it myself.

Very roughly. The chance of pupil number 1 finding that pupil number 2 has the same birthday 1/366. The chance of having the same birthday as any one of the other 24 pupils in the class is 24 times that, 24/366, or about 1 in 15.

So repeat the check for every pupil and you would expect to find a duplicate before you've got to pupil 25.

[QuartzDad]

NoisyGriff said:

Any chance you could run me through the maths behind this? I'm sure you're right, but I can't quite fathom it myself.

Chance of picking two random people who have different birthdays: 364/365

Number of different pairs you can make from 23 people = 253

(364/365) ^ 253 = 49.95%

So the chance of finding two people who have the same birthday is 50.05%

[TwigtheWonderkid]

Nimby said:

otolith said:

TwigtheWonderkid said:

OK, if all the fields are the same, then sheep 1 could have died in any field . The chances of sheep 2 and 3 both dying in the same field as sheep 1 is ten thousand to one. (100 x 100).

It's quite possible, but unlikely. My guess is something environmental in that field is killing them.

If you insure 100 drivers, and there are three at fault accidents, what is the probability that it's the same driver...

If your car was damaged by a meteorite from Mars, would your premiums increase as "it was more likely to happen again"?

Half right. You would now fall into the bracket of people who have had a non fault claim, and if you take 1000 of them, within those 1000, there will be circumstances that mean they are more likely to claim again. So although you personally would be, your group that you are in would be. Hence you might have to pay more.

Insurance isn't personal. It's based on statistics of groups of similar people.