I am attempting the following problem:
Question: A receptionist at a corporate company receives:
- outside calls at a rate of 3 calls in any 10 minute time frame.
- inside calls at a rate of 4 calls in any 10 minute time frame.
Compute the probability of receiving 2 or more calls in any 2 minute time frame. The calls arrive independently and at random.
Attempt:
- Calculate $\lambda=\frac{7}{10}*{2}=\frac{7}{5}=1.4$
\begin{align} P(X \geq 2) &= 1-P(X<2)\\ \nonumber &=1-P(X=1)-P(X=0)\\ \nonumber &= 1-\frac{e^{-1.4}1.4^{1}}{1!}-\frac{e^{-1.4}1.4^{0}}{0!} \\ \nonumber &= 0.40816... \end{align}