Odds, probabilities and "what's the chances of that?"
Discussion
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....
In general people are not very good with estimating probability (beyond very simple examples).
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....
In general people are not very good with estimating probability (beyond very simple examples).
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. https://www.theguardian.com/commentisfree/2020/oct...
In general people are not very good with estimating probability (beyond very simple examples).
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.
I don’t think this calculation can be correct. Firstly there is no information given on the probability of sheep dying and secondly you would need to consider the probability of different combinations (like the birthday paradox raised ie you only need 23 people in a room for the probability of someone sharing a birthday to be more than 50%. It's quite possible, but unlikely. My guess is something environmental in that field is killing them.
Edited by TwigtheWonderkid on Tuesday 27th October 15:11
The maths for the birthday paradox is not straightforward
http://www.solipsys.co.uk/new/TheBirthdayParadox.h...
Edited by Esceptico on Wednesday 28th October 00:42
Esceptico 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.
I don’t think this calculation can be correct. Firstly there is no information given on the probability of sheep dying and secondly you would need to consider the probability of different combinations (like the birthday paradox raised ie you only need 23 people in a room for the probability of someone sharing a birthday to be more than 50%. It's quite possible, but unlikely. My guess is something environmental in that field is killing them.
Edited by TwigtheWonderkid on Tuesday 27th October 15:11
The maths for the birthday paradox is not straightforward
http://www.solipsys.co.uk/new/TheBirthdayParadox.h...
It doesn't matter where the first one dies.
The second has a 1 in 100 chance of dying in the same field.
The third has a 1 in 100 chance of dying in the same field. Multiply the 2 1 in 100 chances together and it's one in 10,000.
To put it another way. Out of 10,000 such farms with 3 sheep deaths Just 100 will have the second die in the same field as the first. Another hundred will have the third sheep die in the same field as the second, of which just one will die in one of the 100 fields with 2 dead sheep already in it.
If we were considering say 25 such farms and trying to work out whether at least one is likely to have 3 dead sheep in one field, then birthday paradox type calculations would be relevant.
KieronGSi said:
21st Century Man said:
StuntmanMike said:
The chances of anything coming from Mars are a million to one he said.
Hundreds of meteorites of Martian origin have been identified on Earth, with new ones arriving every few years. So it's b
ks 
The chances of anything coming from Mars are a million to one, but still, they come.
alorotom said:
KieronGSi said:
21st Century Man said:
StuntmanMike said:
The chances of anything coming from Mars are a million to one he said.
Hundreds of meteorites of Martian origin have been identified on Earth, with new ones arriving every few years. So it's bks The chances of anything coming from Mars are a million to one, but still, they come.
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....
In general people are not very good with estimating probability (beyond very simple examples).
his about to be wife shares the same birthday as my wife,
random?
Dr Jekyll said:
Esceptico 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.
I don’t think this calculation can be correct. Firstly there is no information given on the probability of sheep dying and secondly you would need to consider the probability of different combinations (like the birthday paradox raised ie you only need 23 people in a room for the probability of someone sharing a birthday to be more than 50%. It's quite possible, but unlikely. My guess is something environmental in that field is killing them.
Edited by TwigtheWonderkid on Tuesday 27th October 15:11
The maths for the birthday paradox is not straightforward
http://www.solipsys.co.uk/new/TheBirthdayParadox.h...
It doesn't matter where the first one dies.
The second has a 1 in 100 chance of dying in the same field.
The third has a 1 in 100 chance of dying in the same field. Multiply the 2 1 in 100 chances together and it's one in 10,000.
There is no need to overcomplicate a very straightforward probability question. This is meat and drink to a half decent yr 6 (last year of primary) maths student.
Forget about sharing birthdays or rice on tiles. None of that more advanced maths (which I understand and can do) applies in this case.
The Moose said:
Esceptico said:
Firstly there is no information given on the probability of sheep dying
The probability of a sheep dying is 1.The odds change if the sheep are not the same, or the fields are not the same.
If, before any of the sheep have died, you say "what are the odds that the first 3 all die in field 47" the odds are then a million to one.
TwigtheWonderkid said:
Exactly. You have 100 identical sheep, one each in 100 identical fields, sooner or later one will die. If it's replaced with another identical sheep, sooner or later the 2nd one will die. There's a 1 in 100 chance it'll happen in the same field. Same with the 3rd sheep. So now 1 in 10K that sheep 2 and 3 both die in the same field as sheep 1.
The odds change if the sheep are not the same, or the fields are not the same.
If, before any of the sheep have died, you say "what are the odds that the first 3 all die in field 47" the odds are then a million to one.
Of course this doesn't take into account sheep psychology. Sheep are herding creatures and will tend to be within close proximity of each other if possible - hence the 1 in 10K is a maximum probability and unlikely to be experimentally reproducible. The odds change if the sheep are not the same, or the fields are not the same.
If, before any of the sheep have died, you say "what are the odds that the first 3 all die in field 47" the odds are then a million to one.
Any experiments involving sheep and counting are dangerously soporific and should only be attempted by professionals or insomniacs
Jinx said:
Of course this doesn't take into account sheep psychology. Sheep are herding creatures and will tend to be within close proximity of each other if possible - hence the 1 in 10K is a maximum probability and unlikely to be experimentally reproducible.
No, this doesn't take into account that sheep are the most stupid creatures out and if they can find a way to die they will. Any experiments involving sheep and counting are dangerously soporific and should only be attempted by professionals or insomniacs
It doesn't stop them being adorable as lambs though, or great with mint sauce!
Mammasaid said:
Jinx said:
Of course this doesn't take into account sheep psychology. Sheep are herding creatures and will tend to be within close proximity of each other if possible - hence the 1 in 10K is a maximum probability and unlikely to be experimentally reproducible.
No, this doesn't take into account that sheep are the most stupid creatures out and if they can find a way to die they will. Any experiments involving sheep and counting are dangerously soporific and should only be attempted by professionals or insomniacs
TwigtheWonderkid said:
We have to assume all 100 sheep have the same psychology, and are equally stupid. In which case, the maths still works.
A farmer has some chickens who don't lay any eggs. The farmer calls a physicist to help. The physicist does some calculation and says "I have a solution but it only works for spherical chickens in a vacuum!21st Century Man said:
StuntmanMike said:
The chances of anything coming from Mars are a million to one he said.
Hundreds of meteorites of Martian origin have been identified on Earth, with new ones arriving every few years. So it's bks 
TwigtheWonderkid said:
Bluesgirl said:
Surely it’s 10,000 to one that sheep 2 dies in the same field, but 1,000,000 to one that the third sheep dies there too.
Nope. It's a million to one chance for you correctly pick a field for all 3 to die in, before the first one has died. But in this case, the 1st one can die in any field. The chances of the next 1 dying in that field are 100/1. The chances of the next 2 dying in that same field are 10,000/1. 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?
Insufficient data given. 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?
OP, you have not quoted the number of sheep: it could be just three.
If they were constantly kept in just one of the fields, they would inevitably die there within the 17 year period, which exceeds the natural lifespan of a sheep. Or they could all be attacked and killed by dogs in one awful event.
So under those circunstances there is no question of chance, it's a certainty.
glenrobbo said:
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?
Insufficient data given. 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?
OP, you have not quoted the number of sheep: it could be just three.
If they were constantly kept in just one of the fields, they would inevitably die there within the 17 year period, which exceeds the natural lifespan of a sheep. Or they could all be attacked and killed by dogs in one awful event.
So under those circunstances there is no question of chance, it's a certainty.
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