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Answer:
a. 0.563 = 56.3% probability that for the next 60 minutes (two time periods) the system will be in the delay state.
b. 0.625 = 62.5% probability that in the long run the traffic will not be in the delay state
Step-by-step explanation:
Question a:
The probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.75.
The system currently is in traffic delay, so for the next time period, 0.75 probability of a traffic delay. If the next period is in a traffic delay, the following period will also have a 0.75 probability of a traffic delay. So
0.75*0.75 = 0.563
0.563 = 56.3% probability that for the next 60 minutes (two time periods) the system will be in the delay state.
b. What is the probability that in the long run the traffic will not be in the delay state? If required, round your answers to three decimal places.
If it doesn't have a delay, 85% probability of continuing without a delay.
If it has a delay, 75% probability of continuing with a delay.
So, for the long run:
x: current state
85% probability of no delay if x is in no delay, 100 - 75 = 25% if x is in delay(1-x). So
0.625 = 62.5% probability that in the long run the traffic will not be in the delay state