What determines the accuracy of a probability estimate based on repeated trials?

[Likith D]

If you go through my thread here
https://www.physicsforums.com/threa...the-phenotypic-ratio-of-the-pea-plant.848650/
There is a particular reason that strikes me when i go through the answers i received - it seems so that for each pea to grow into a tall plant, the possibility of such an event is 3 for 4; and the probability of the pea to grow to a dwarf one is 1 for 4...
lets consider a similar sort of experiment, Mendel took
Say I have a die and 5 of it's faces are painted green and the other 1 is painted yellow, and you don't know the number of faces the die has ( say ). Only by rolling the die and noting observations can you guess the number of faces a die has for X number of trails and ;
will greater the X , more accurate the guess ?

 

[Hornbein]

If you go through my thread here
https://www.physicsforums.com/threa...the-phenotypic-ratio-of-the-pea-plant.848650/
There is a particular reason that strikes me when i go through the answers i received - it seems so that for each pea to grow into a tall plant, the possibility of such an event is 3 for 4; and the probability of the pea to grow to a dwarf one is 1 for 4...
lets consider a similar sort of experiment, Mendel took
Say I have a die and 5 of it's faces are painted green and the other 1 is painted yellow, and you don't know the number of faces the die has ( say ). Only by rolling the die and noting observations can you guess the number of faces a die has for X number of trails and ;
will greater the X , more accurate the guess ?

Yes, the accuracy of the guess increases with the number of trials. This is what statistics is largely about, telling you exactly how (in)accurate.

 

[WWGD]

If you go through my thread here
https://www.physicsforums.com/threa...the-phenotypic-ratio-of-the-pea-plant.848650/
There is a particular reason that strikes me when i go through the answers i received - it seems so that for each pea to grow into a tall plant, the possibility of such an event is 3 for 4; and the probability of the pea to grow to a dwarf one is 1 for 4...
lets consider a similar sort of experiment, Mendel took
Say I have a die and 5 of it's faces are painted green and the other 1 is painted yellow, and you don't know the number of faces the die has ( say ). Only by rolling the die and noting observations can you guess the number of faces a die has for X number of trails and ;
will greater the X , more accurate the guess ?

Have you read about the Law of Large Numbers?

 

[Likith D]

Have you read about the Law of Large Numbers?

nope but i'd be interested...

 

[Stephen Tashi]

will greater the X , more accurate the guess ?

In a scenario involving probability there are no deterministic guarantees. You can't be sure the guess will be more accurate with a greater number of trials. The correct statement is that more trials implies a greater probability that the estimate ("the guess") will be accurate.

 

[Likith D]

In a scenario involving probability there are no deterministic guarantees. You can't be sure the guess will be more accurate with a greater number of trials. The correct statement is that more trials implies a greater probability that the estimate ("the guess") will be accurate.

That makes it more clear
Thanx