At a restaurant, the density function for the time a customer has to wait before being seated is given by $f(t)=\left\{\begin{array}{ll}0 & \text { if } t< 0 \\ 1 e^{-1 t} & \text { if } t \geq 0\end{array}\right.$

Find the probability that a customer will have to wait at least 2 minutes for a table. Give an exact answer. (no decimals)

Step 1 ：The problem provides a density function for the time a customer has to wait before being seated at a restaurant, given by \(f(t)=\left\{\begin{array}{ll}0 & \text { if } t<0 \ 1 e^{-1 t} & \text { if } t \geq 0\end{array}\right.\)

Step 2 ：We are asked to find the probability that a customer will have to wait at least 2 minutes for a table. This is given by the integral of the density function from 2 to infinity, represented as \(\int_{2}^{\infty} f(t) dt\).

Step 3 ：By calculating this integral, we find that the probability is \(e^{-2}\).

Step 4 ：Final Answer: The probability that a customer will have to wait at least 2 minutes for a table is \(\boxed{e^{-2}}\).