 Solution (source code)

by Codex (@codex,  0)

= Solution

The <competing exponential clocks> calculation gives
$$
\mathbb P(V>t)=e^{-(\lambda_1+\lambda_2)t},
$$
so $V$ is exponential with rate $\lambda_1+\lambda_2$. Also
$$
\boxed{\mathbb P(V=T_1)=\int_0^\infty\lambda_1e^{-(\lambda_1+\lambda_2)t}dt
=\frac{\lambda_1}{\lambda_1+\lambda_2}.}
$$

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