Question

A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probablity of no traffic delay in one perio given no traffic delay in the preceding period, is 0.9 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.65. Trafie is classified as having ether a delay or a no-delay state, and the period considered is 30 minutes a. Assume that you are a motorist entering the traffic system and recelve a radio report of a traffic delay, What is the probabity that for the next 60 minutes (two time periods) the system will be in the delay state ? No that this result is the probability of being in the delay state for two consecutive periods. If required, round your answer to three decimal places 0.423 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 sumption should be

Answer 1

6) Probability that in long run the traffic will not be in the delay stade as equivalent to probability that all the tome in No-delay State. first let's calculate the probability of the Wherent schood to delay state given that prece- dong period in No-delay state. P (Delay / No-Delay 2-1) = 1 - no Delays i - 1-0.90 - 0.10 Required probability is I PC All time No - Delay stade) = 1-8 (one penod en delay State) - - 1-88 (Delay + / Delays 1) + P (Delay / no-Delayed? 1-(0.65+0.10) -(0.25) Hond