I am trying to do probability exercises but when it is not Binomial I am kinda lost.
A parking lot had two entrances. On average, a car arrives at entrance 1 of the parking lot every $20$ minutes and a car arrives at entrance 2 of the parking lot every $15$ minutes. We suppose that the number of cars arriving at entry 1 is independent of the number of cars arriving at entry 2. Given that $3$ cars entered the parking lot today between 14h and 15h, what is the probability that entrance 2 has seen more cars arriving during this period than entrance 1 ?
E(entrance 1)= 20 E(entrance 2)= 15 P(e2 > e1 knowing there are $3$ car between in $60$ min)
I don't even know where to start. Is it conditional? I thought about the Poisson distribution but because of the second entrance I don't see what to do. Is it really a Poisson distribution?