City buses are numbered sequentially 1, 2, ..., M. If M were known, and Y represents the number on the next bus you see, find an expression for P(Y = y|M).
I think that P(Y = y|M) = $\frac{1}{M}$ since for y = 1, 2, ..., M. Is this correct? I think that this is true because we know that there are M total buses, so the probability that the next bus you see has a specific number on it is one over the total number of buses.
Assuming that the next bus you see is entirely random, then yes. $P(Y=y|M)=\frac{1}{M}$. If the buses are not entirely random, you need more information to determine the actual probability.