The number of people arriving for treatment at an emergency room can be modelled by a Poisson process with a rate parameter of five per hour. What is the probability that more than 12 people arrive during a two hour period?

I said $\displaystyle >12$ people arriving in 2 hours would be the same as finding $\displaystyle >6$ people in one hour using the same parameter $\displaystyle \lambda = 5$

Using $\displaystyle P(X) = \frac{e^{-\lambda}\lambda^x}{x!}$

$\displaystyle P(X>6) = 1- P(X\leq 6) = 1-0.762 = .238$

but this was not correct. I think the problem here is my logic.