There is a bag of $n$ coins. 1 of the $n$ coins is golden. You draw a coin, record it, and put it back in the bag. What is the probability that after $k$ such draws, you have drawn the golden coin at least once?
Is it just $(\frac{n - 1}{n})^k$? I am supposed to give the answer in the form 1 - $x$ for some x, so I am confused if I am on the right track.
Yes, you're on the right track. The probability of picking it at least once is 1- the probability of never picking it, so:
$P = 1-(\frac{n-1}{n})^k$