I'm having a bit of trouble understanding exactly why there is a "1" in the general simple Binary Choice Model where $Y_i$ can take a value of either $0$ or $1$. We also assume that the conditional distribution of $\epsilon$ given $X$ is a standard normal distribution.
For example, in my notes, our econometrics professor wrote the following:
$$E[Y_i|X_i=t]=P[B_0+B_1X_i\geq\epsilon_i|X_i=t]$$ and the next step was: $$E[Y_i|X_i=t]=E[1(B_0+B_1X_i\geq\epsilon_i|X_i=t]$$
My question is about this $1$ that keeps popping up. What is the significance of this? Also How can we go from the line above to the line below?