What’s the probability that exactly $12$ buses will arrive within $12$ hours

Let’s suppose there are two buses number $ 86$ and $ 98$ . They draw up at the bus stop under the Poisson distribution with intensities $ 3$ and $ 5$ times per hour. (a) What’s the expected length of time after the $ 15$ th bus will arrive?, (b)What’s the probability that exactly $ 12$ buses will arrive within $ 12$ hours?

Poisson distribution $ P(N(t)=j)=\frac{(\lambda t)^j}{j!}e^{-\lambda t}$ . We have that $ j =3$ or $ j =5$ . Do I just substitute $ j =3$ and $ \lambda t=15$ and we immediately have (a)? I’m aware that’s a really easy exercise but I somehow don’t really know how to approach this one. I’m also not sure how to approach subpoint (b). I’ll be thankful for any tips and help.

Do buses run on May 1st in Bavaria?

I am interested in landing in Munchen on 1st of May, and then take the bus to Ingolstadt. Does the bus operate in 1 May (since I am only interested in Airport-ZOB Ingolstadt)?

I guess it will be sparser, but that’s OK. I don’t want to book a flight and then find out that there is no bus! I pretended booking a ticket for the bus, but the system says its far too early, so doesn’t really answer the question.