Statistics and Probability

There are three colors of cars, red, green, and blue, which enter a certain checkpoint with the Poisson flows with strengths 1, 2 and 3, respectively. Assuming they are independent of each other, combine the car streams into a single output process (assuming cars have no length, no delay)

(1) Try to find the probability density function of the time interval between two cars;

(2) Try to find the probabilities for observing a red car at time to, the next car being 1 red; 2 blue; 3 not being red;

(3) Try to find the probability of the case that after observing a red car at time to, the next three arriving cars are red, and then another non-red car will arrive.