I'm an amateur with some interest in statistics and I would appreciate it if anyone could verify that I didn't make any mistakes on how I tried to tackle a specific problem I encountered, or give me suggestions for a better solution. Because I'm unsure I'm not misusing terms (English is not my first language), I'll try to be as descriptive as possible, so please bare with me. My situation is as follows:
I have a number of coins that have different chances of success (ranging from 0% to 100%). I define a random variable X where success gives 1 point, while a failure gives no points.
I now define an experiment, where I pick a specific series of coins, and declare how many times should each coin be tossed, and the order of the coins being tossed. (So for example, I define an experiment where I toss a coin with 30% success rates 50 times, then a 20% coin 6 times, then a 3% coin 2 times). I add up all of the score obtained during the course of the experiment.
What I'm interested in finding out is the following:
How 'likely' it is for a person conducting the experiment to botch all of their tries, i.e. ends with a score that is exactly zero.
A measurement of how 'spread' the experiment is, or "what would be reasonable scores to expect most people to get".
What I tried to do is as follows: For the first question, for each coin I took the failure rate, took it to the power of the number of tosses conducted on that specific coin (I think about this as the chance of failing all of these successively), then multiplied those chances between all of the coins. I think of the end result as "this is the chance that a person taking this experiment will get exactly 0".
For the second question, I multiplied the success chance of each coin with the number of tosses that specific coin has (I think about this as the expected value of all of the tosses of that coin E[X]), then added up those values for all of the coins, divided by the number of coins to obtain the average for all of the tosses on a coin, then for each coin raised to the power of 2 the difference between the expected value of all of the tosses of that coin and the average value for all of the tosses on a coin, summed those, divided by the number of coins, and took the square root (this should give me the standard deviation).
I think about this as 'most people score fall within the sum of all expected values of each coin, +- the standard deviation'.
Problems I have:
A. Sanity check: On the first question, would getting an end result of 20% mean "if a billion people took the experiment, you can expect about 20% of them to fail and 80% to succeed?"
B. On the second question, I'm not sure which makes more sense: calculating the average/standard deviation on all of the tosses on each coin, or maybe I should calculate those values on each toss.
C. I faced an experiment where all coins are identical and rolled the same number of times, and I got a standard deviation of zero. I doublechecked my math and didn't find any errors, but it intuitively doesn't make sense to me: If a number of people would perform the experiment, I'm sure not all of them with perfect accuracy get the expected value. Were I to draw a graph of all the results, I'd expect some sort of spread, with most results being near the average but not all being exactly the average. In a sense, I'm trying to find a metric for the "tightness" of said graph, and a standard deviation of 0 doesn't make sense for me in this context. This gives me one of three options: Either there's something wrong with my math, I didn't calculate the standard deviation on the right parameter, or standard deviation isn't what I think it is.
D. Something I really want to answer for both 1 and 2 is to be able to say a certain result with some sort of 'confidence' i.e. x% of people taking the experiment would score higher than such and such score. I've tried looking things up, I think what I'm looking for is called a probability density function. It's somewhat difficult for me, but from what I understand those seem to take huge data sets and generate graphs from them, and while I probably could try and perform the experiment a couple of times and write down the results, this seems both tedious and backwards to me and, and would needlessly introduce randomness. Another problems I have with it is that I sometimes have coins with 100% probability, so they give a hard minimum to the experiment score - but the curves on those functions seem to be a perfect curve and always have some chance of scoring below a certain number.
I would appreciate it if I could be told whatever I'm in the right direction, what to look into, or a guide on how to perform the relevant calculations.