If I have a set of events $A_i$ for which $Pr[A_i] = \frac{1}{n-1}$ for all i. I am trying to come up with an example of these events that fulfill this prob. I also want that the prob of none of them occurs = zero.
My first guess was:
n can be {1.......2n-2}
for $A_1 ......A_n$
$A_i$={i,i+1}
Is my guess correct? if yes how can I proof it?
Thanks
Your guess is close and more complicated than you need. If you draw an $n$ uniformly from $[1,2n-2]$ and assign it to $A_i$ when $i \in \{n, n+1\}$ you will never find $A_n$ is true. As you need the probabilities to add to $1$, there must be $n-1$ of them. A simple example is $n=3$ and flipping a coin. Heads and tails have probability $\frac 1{n-1}=\frac 12$ A standard die and $n=7$ works as well.