I want to calculate the probability:
\begin{equation*} P(W_4>2, \inf_{0\leq t\leq4} W_t >-1) \end{equation*}
and $W$ is a Wiener process.
I tried:
\begin{equation*} P(W_4>2, \inf_{0\leq t\leq4} W_t >-1)= P(W_4 >2)-P(W_4>2 \inf\ W_t <-1) \end{equation*}
Then applying the reflection principle
\begin{equation*} =P(W_4 >2)-P(W_4 <-3)= \phi(4/3)-\phi(1) \end{equation*}
But my textbook says the solution should be: $\phi(2)-\phi(1)$.
What did I do wrong?