What are some common issues to think about when evaluating an assumption made about the probability of something?

When calculating a probability, we assume that there is only one outcome for each trial and that each trial has the same probability of success. issues for that include: It is unrealistic to assume that the probability of success is consistent, and the fact that each trial has only one outcome.

Data has linear relationship. Data is independent

is the probability of each trial the same for example in the Binomial distribution?

are trials independent of each other, eg) for a binomial question where someone is hitting the bullseye using darts you would expect the probability to change since in this situation the more times you practice the higher the probability would be.

When evaluating the probability of events, the most common assumption made is that all trials are independent of each other. Another assumption would be that the probability of all the events we deem possible sum to 1, when often we omit certain possibilities (e.g. flipping a coin, we believe it lands either heads or tails with probability half, but it could land on its side). Instead, we could do better by saying the probability of the coin landing heads given that it does not land on its side is 0.5 and similarly for the coin landing on tails.

we make assumptions that one time produce one probability .for example two sides of coin .the probability of front is 1/2 .

Often our assumptions of relative probabilities are dependent on how much information we have and prone to bias. A common issue is to misinterpret or misrepresent the available information to conclude what a probability intuitively "must be". For example the famous Monty Hall problem, whereby opening one of three doors revealing the hidden contents intuitively feels as if the probability of your original choice being the winning door has changed to a half, when in actuality it remains one third, unchanged by the new information. The chance of the "other doors" being winning is still 1 - 1/3 = 2/3, but what has changed is how many "other doors" there are, one instead of two, so you should always switch your door choice. This reveals another bias; assuming that all the possible outcomes or macro states have the same probability.

You may have to assume that the probability is not conditional. Or else use the use the condition in evaluating the probability.