I am trying to find out what the probability is that my order is finished earlier when I put it through one machine that on Poisson distribution finished lambda = 3 orders per hour vs. two machines that have lambda1 = 8 per hour and lambda2 = 10 per hour but in this scenario you have to pass through both machines subsequently!
I understand that on option 1 my expected time is 1/3 of an hour but I am struggling how to find the probability that this is quicker than by using the two faster machines that have to be used both after each other. Especially how exactly I use the Poisson distribution here with the question of "probability that option 1 is faster".