When cycling home at night, I notice that sometimes my rear light is switched oﬀ when
I arrive home. Presumably the switch is loose and can ﬂip from on to oﬀ or back again
when I go over bumps. I suppose that the number n of ﬂippings per trip has a Poisson
distribution (e^−λ)(λ^n) /n!. If the probability that the light is still on when I arrive home is p, ﬁnd λ.

Hi, new to the forum and don't know how to use symbols here but I have the answer so I will hack at it will Latex. It is not that hard once you realize there must be a simplificaiton if you want to solve for λ analytically. Basically you are given the probability that the distribution is even.