A road traffic light is switched on every day at 5:00 a.m. It always begins with red and holds this colour for two minutes. Then it changes to yellow and holds this colour for 30 seconds before it switches to green to hold this colour for 2.5 minutes. This cycle continues till midnight.

(1) A car driver arrives at this traffic light at a time point which is uniformly distributed between 9:00 and 9:10 a.m. What is the probability that the driver catches the green light period?

(2) Determine the same probability on condition that the driver's arrival time point has a uniform distribution over the interval [8:58, 9:08].

Transcribed Image Text:

H 9:00 red + 9:02 greeny, red 9:04 + 9:06 greeny, ++ 9:08 9:10 8.58 green y red ++ 9:00 greeny red green 9:02 9:04 9:06 9:08