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If this is the only information that you have then you must use the Poisson distribution.
Random Variable in probability theory is defined as follows: Assuming you have variables Xi where i is an integer ie: i=1,2,3.......n a variable Xi is called a random variable iff(if and only iff) and random selection yields a variable Xi for i=1,2.........,n with the same likelihood of appearance. i.e prob(X=Xi)=1/n
Not sure about only two requirements. I would say all of the following:there is a finite (or countably infinite) number of mutually exclusive outcomes possible,the probability of each outcome is a number between 0 and 1,the sum of the probabilities over all possible outcomes is 1.The Poisson distribution, for example, is countably infinite.
If only one card is selected the probability is 12/13.If only one card is selected the probability is 12/13.If only one card is selected the probability is 12/13.If only one card is selected the probability is 12/13.
Since the word "probability" contains only letters, then the probability of choosing a letter from the word "probability" is 1, i.e. it is certain to happen.