Suppose I have 6 different coins that have wildly different increasing chances of flipping a heads, and I know the chances of flipping a heads for each.
(ie. Coin 1: 1/280 chance of heads ... Coin 6: 1/120 chance of heads)
Without looking, if I choose one of these coins at random and flip it some limited number of times, how can I determine the probability it is each of the 6 coins in relation to each other from the results alone?
(ie. A result like [Coin1: 5%, Coin2: 7%, Coin3: 10%, Coin4: 14%, Coin5: 25%, Coin6: 39%])
My statistics knowledge is limited to what I learned in first year university, so I originally thought I could solve this problem using the chi-square test with the expected results of each of the 6 coins. The problem is this gives me the probability that the results were simply due to chance vs it not actually being that coin (possibly not even one of the original 6 coins, when I know it must be one of the 6 coins!).
So for example if I flipped a coin 10,000 times and (by some extreme chance) every result was a heads, I should be getting a result reporting the confidence of coin 6 as being something extremely high with a very tiny % chance of being coin 1 to 5. Instead the result I get is that there's a 0.000001% or so chance of it being any of the 6 coins at all.
Am I using the wrong approach to solving this problem?