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.

Thanks.