I am just gonna quickly recap for you so you stop annoying me with your pings on this dead topic. This whole conversation started when I mentioned that the way to look at x% probability is that you just expect to try 1/x times to see a success on average.
Now, this statement had nothing to do with you nor was even for you. Yet, you just couldn’t help but say this is incorrect, saying I must be working at Burger king to come to this conclusion while also claiming you were a data scientist who was familiar with probability.
Being a busy person, I just asked you to google it up. Obviously you didn’t. Now, onto the point. You can prove that the expected number of trials to see a success is 1/p if p is the probability of success, which you replied that I must work at burger king to think this is so.
At 1st try, a successful outcome will occur with a probability p.
If 1st fails, a successful outcome can happen with a probablity (1-p)p.
If 2nd attempt fails, it will then occur on the third try with probability (1-p)(1-p)p…
The probability that nth trial is the first success is …
P(X=n) = (1-p)^n-1 * p
And this is called Bernoulli’s trial. You can look up wiki on Bernoulli’s trial and you will see exactly this. It is an elementary stuff in any probability textbook.
Now that I have shown that this honing we do is a Bernoulli trial… all we gotta do is look up the expected value of this geometric distribution.
Due to mathematical notation being hard to type it out, you can find the proof that E[X] = 1/p can be found here:
And here you are asking about whether the probability of failing n is (1-p)^n, and I never even disagreed with the statement. But I guess that’s all you know and that’s why you keep coming back to that stupid formula.
And also you said the probability of at least one of 10 tries being successful would be 65%. But you stop when you are successful. Also, you need to understand that the probability you are calculating here is retroactive in nature, and the chance of hitting the next honing is 10% REGARDLESS of how many failures in a row you have experienced so far.
Here is a really f*cking simple way to look at this.
Say you flipped coin 10 times and you got tail tail tail tail … and all tail.
Now you gotta flip a coin one more time. What is the chance that you get a tail?
It is a freaking 50 percent still. If for some reason you thought because you flipped coin 10 times already and got all tail, you think the probability of getting the 11th tail is 0.5^11, you are getting it wrong.
The chance of getting all 11 flips to be tail would be 0.5^11 but the next flip will always be 0.5 regardless of the past results.
Edit: some typos