Hotel has ten rooms, on average 7 are booked per night.
Website enables twelve bookings to be made on a given night.
What is the probability they'll not be able to accommodate all guests on given night.
State any assumptions you make.
**My initial thoughts were poisson. P(11) + P(12) guests show up on a night which is 7.2% and assumption being all bookings are independent.
Any help appreciated
Here is how you can use Poisson distribution: $$\mathbf P(X=k)=\frac{\lambda^k}{k!}e^{-\lambda}$$ where $X$ is the random variable that deals with the no. of guests in the hotel. Note that $\lambda=7$.
The answer is therefore: $$\mathbf P(X\geq 11)=1-\sum_{k=0}^{10} \frac{\lambda^k}{k!} e^{-\lambda}$$ because we know that the hotel cannot accommodate more than $10$ guests.