Say we have the following problem:
We are flipping some coin. The probability of it landing on heads is $p$. Is the expected number of coin flips we need to get the expected number of heads to be 1 different from the expected number of coin flips we need to get one head?
P.S. when I say are they the same I mean are they equivalent questions, not are the values of both the same (which they are).
I would think these are the same but I don't know how to describe why.
Thanks in advance :)