I have two sets, say $S_1 = \{1, …, n\}$ and $S_2 = \{0, 1, …, n – 3\}$
How do I find the probability that randomly selected numbers $n \in S_1$ and $m \in S_2$ are equal?
[Math] probability that two randomly selected numbers are equal
probability
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Best Answer
Well, your elementary event implies selecting of a number from $S_1$ and another (maybe equal, maybe not) number from $S_2$. There are $n\cdot(n-2)$ such events, and $n-3$ of them lead to the desired outcome (i.e., that the numbers are equal). Hence the probability in question is $n-3\over n(n-2)$.