What methods can I research to help me estimate a probability This is my first question on here, I hope it goes well... I need to estimate the probability of an event that I don't have historical data on, but I do have data on similar/comparable events. I hope this is not too general. For example, take the damage rate of one item with one particular; this is a simple count, did the item get damaged--Yes/No and convert to a rate. I believe this data is characterized by a binomial distribution. Is there a method that I can apply to estimate the damage rate of another similar item based off the item I do have data on??

A sample represents the population it is drawn from. The question becomes how much similarity there is between the population you observed, and the population you didn't observe but want to reason about. Suppose you have a box of Item X and can observe the damage rate. You may or may not be able to use that as an estimate for Item Y, depending on how similar they are. If Item X and Item Y are similar transistors both made by a particular company in a particular time period with the same equipment, it's reasonable to guess that they might be damaged at the same rate - you're effectively suggesting that Item X can be used to reason about the wider population of transistors, rather than just the population of Item X transistors. But if Item X  is a transistor, and Item Y is a chicken egg, you'd expect entirely different processes to be responsible for damage, so you couldn't reasonably guess at the damage rate of one from the damage rate of the other.
There's nothing in the data itself that can tell you whether the observed rate is a decent proxy for the unobserved rate. It will require understanding of the underlying processes, and how similar those are between the two items you want to compare. The damage rate of transistors made by one company will probably be a decent guess at the damage rate of other transistors from that company, a less useful guess at the damage rate of transistors made by a different company, and a useless guess at the damage rate of chicken eggs.
