Unforgeability proof of partially blind signature (schnorr signature based)

Question

I read a representative paper about partially blind signature.

Abe and Okamoto - "provably secure partially blind signature".

They suggested a partially blind signature scheme based on Schnorr signature.

But I cannot understand the proof of Lemma 2 that the scheme is unforgeable.

Below image is part of the proof process. (p.281)

${M}$ is a machine constructed by a forger ${U^*}$, y is public key where ${y=g^x}$, ${F, H}$ is random oracles, and ${Info}$ means message.

Why ${M}$ outputs a valid signature with probability at least ${1-e^{-1}}$? (highlighted part)

Thanks.

Answer 1

If the probability (over random choice of the random tape $\rho$ and the random oracle $\mathcal{H}$) of a particular trial being successful is at least $\mu'$, then the probability that $1/\mu'$ independent trials* are unsuccessful is at most $(1-\mu')^{1/\mu'}$ --- this expression converges to $1/e$. The claim follows.

*Here, independence refers to the choice of $\rho$ and $\mathcal{H}$.