The ferry crosses the strait from beach A to beach B at regular intervals of 20 minutes. The ferry has room for 7 cars.
Suppose no cars left behind when ferry first leave. Suppose the number of cars arriving on the beach A the next 20 minutes in the following cases is the Poisson distribution parameter 6.
What is the probability that the ferry will be full the next time it leaves at beach A?
Should i use poisson distribution and is lambda on this case the 6?
\begin{align} \mathbb P(X\geqslant 7) &= 1-\mathbb P(X<6)\\ &= 1-\sum_{k=0}^6 \mathbb P(X=k)\\ &= 1-\sum _{k=0}^6 \frac{6^k}{k!}e^{-6}\\ &=1-\frac{1223}{5}e^{-6}\approx 0.3936972. \end{align}