Cars approach a traffic light according to a homogeneous Poisson process with rate =300 per hour. (a) At the moment the light changes from green to red, there are no cars waiting at the light, and the red light lasts for one minute. Find the probability there will be at least one car waiting before the light turns back to green. (b) The green/yellow light lasts for a total time of two minutes in each cycle. From 12:00pm until 12:01pm, the light is red. Find the probability that the total number of cars passing through the light between 12:01pm and 12:03pm and 12:04pm and 12:06pm is exactly 10. (c) BONUS: It is desired to have as few cars at the light when the light is red as possible. Accordingly, the red light period is shortened to increase the chance of there being zero cars present throughout the duration of the red light period. Find the largest time interval for the red light so that there is at least a. 50% chance no cars appear during this interval. Give your answer in seconds correct to four decimal places