Paul --- A Rock and a Hard Place

[Kunigunde Kreuzerin]

I will let the reader decide whether this is the best model for settling the questions themselves...

I simply trust you. It's easier for me

[Bernard Muller]

Peter is right:
http://able2know.org/topic/352494-1 (my second opinion)
For 6 independent arguments with for each 20% chance to prove the same point, the overall chance for these 6 arguments put together to prove the point is 73.7856%.
Thanks Peter & Ben,

Cordially, Bernard

[iskander]

The Binomial distribution is a model for a Bernoulli trial .

[Ben C. Smith]

Peter is right....

Shocker.

[MrMacSon]

Peter is right....

Politically? Did he vote for Trump??!

[Peter Kirby]

The Binomial distribution is a model for a Bernoulli trial .

If you just want a single "Bernoulli trial," you would use the "Bernoulli distribution":

https://en.wikipedia.org/wiki/Bernoulli_distribution

Which is really an over-complicated way of saying "an event that occurs with probability p."



Here, "k=1" is the success event (probability p) and "k=0" is the non-success (probability 1 - p).

https://en.wikipedia.org/wiki/Bernoulli_distribution

The Bernoulli distribution is a special case of the two-point distribution, for which the two possible outcomes need not be 0 and 1. It is also a special case of the binomial distribution; the Bernoulli distribution is a binomial distribution where n=1.

https://en.wikipedia.org/wiki/Binomial_distribution

The Bernoulli distribution is a special case of the binomial distribution, where n = 1. Symbolically, X ~ B(1, p) has the same meaning as X ~ B(p). Conversely, any binomial distribution, B(n, p), is the distribution of the sum of n Bernoulli trials, B(p), each with the same probability p

I don't think that this is helpful in the context of this thread. The terminology of "Bernoulli" trial/experiment is a lot more work (for those not comfortable with the terminology) than it's worth, for describing an extremely simple concept.

(If there is a point to be made here, I'm open to being shown what it is.)

[Peter Kirby]

I will let the reader decide whether this is the best model for settling the questions themselves...

I simply trust you. It's easier for me

Okay then, here it is in a nutshell.

Arguments that "prove a point" with a probability of X% (where X is low) is a slippery concept. I'm guessing that this means (using one interpretation of probability), that whenever arguments like this are used, they are found to prove the point 20% of the time. But that seems extremely odd.

It comes back to what it means to "prove a point," which is to make it certain or virtually certain that it is true. I could understand saying that I have an argument that has a 99% probability of proving a point. Maybe, in the past, arguments like this one (which have been checked by two people) have stood the test of time as arguments that prove the point. For example maybe these are papers that make it to print in mathematics. Maybe 1% of them are found later not to prove the point (a step of the proof was eventually found false -- so it failed the 'truth' criterion of knowledge, despite adequate justification for belief). But the remaining ones did. Or maybe they are DNA analyses or something similar.

But 20% chance to prove a point? It's a startling claim. It's like saying that there's a 2% chance that a baby can guard Fort Knox with absolute security, or that there's a 4% chance that a crook can be trusted with your money with absolute confidence. It just sounds silly. Only under contrived circumstances could you make statements like that (e.g., maybe a computer program generating arguments could spit out proofs with probability 20% or something).

Maybe there's a way to make use of these arguments, maybe a way to do so in a probabilistic setting, but they are not "proving" any points.

We too easily allow ourselves to make contradictory assumptions when we let in slippery concepts like this. Imagine two people arguing a topic. Each has six arguments. Each of them insists that they must be allowed at least a 20% chance for their respective arguments to succeed (and that these probabilities are independent). Well, that's a contradiction. And our concept of "proving a point" or not, will not allow us to have an easy time of weighing both sides of an argument where there is uncertainty (not proof, only indications of a probabilistic nature).

Math doesn't say anything about how we have to model things like this. (Creating a model requires domain knowledge. It's not just math.) So I'm not going to say that there is just one solution. But I think we need to try harder than this.

[iskander]

The Binomial distribution is a model for a Bernoulli trial .

If you just want a single "Bernoulli trial," you would use the "Bernoulli distribution":

https://en.wikipedia.org/wiki/Bernoulli_distribution

Which is really an over-complicated way of saying "an event that occurs with probability p."



Here, "k=1" is the success event (probability p) and "k=0" is the non-success (probability 1 - p).

https://en.wikipedia.org/wiki/Bernoulli_distribution

The Bernoulli distribution is a special case of the two-point distribution, for which the two possible outcomes need not be 0 and 1. It is also a special case of the binomial distribution; the Bernoulli distribution is a binomial distribution where n=1.

https://en.wikipedia.org/wiki/Binomial_distribution

The Bernoulli distribution is a special case of the binomial distribution, where n = 1. Symbolically, X ~ B(1, p) has the same meaning as X ~ B(p). Conversely, any binomial distribution, B(n, p), is the distribution of the sum of n Bernoulli trials, B(p), each with the same probability p

I don't think that this is helpful in the context of this thread. The terminology of "Bernoulli" trial/experiment is a lot more work (for those not comfortable with the terminology) than it's worth, for describing an extremely simple concept.

(If there is a point to be made here, I'm open to being shown what it is.)

binomial experiments,
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.. and the six arguments of Bernard cannot be accepted as an n.

There are only 2 possible outcomes, called "success" and, "failure" for each trial. The letter p denotes the probability of a success on one trial and q denotes the probability of a failure on one trial. p+q = 1.

The n trials are independent and are repeated using identical conditions. Because the n trials are independent, the outcome of one trial does not affect the outcome of any other trial.

[Peter Kirby]

The letter n denotes the number of trials.. and the six arguments of Bernard cannot be accepted as an n.

Great. Maybe I agree -- surely more than willing to agree here (having come to this conclusion, apparently, by a different route). But you haven't explained why you say that. Equivalently, what do you believe about "arguments" that means that they cannot be considered "Bernoulli trials"? Is it the idea that they have a "probability" at all? Is it the idea that we have this probability figure? Is it independence?

PS-- You're plagiarizing. Makes me wonder how steady you are on all of this.

https://cnx.org/contents/vGiLOvP5@6/Bin ... stribution

There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes, called "success" and "failure," for each trial. The letter p denotes the probability of a success on one trial, and q denotes the probability of a failure on one trial. p + q = 1.
The n trials are independent and are repeated using identical conditions. Because the n trials are independent, the outcome of one trial does not help in predicting the outcome of another trial.

[spin]

PS-- You're plagiarizing.

Gee, that's stiff. He's just not attributing. It's hard to get people to cite. Besides, plagiarizing only really applies to more formal circumstances. Have a chocolate.