You arrive at McDonald's of the First Student Activity Center and find that there are two long lines (Line A and Line B)

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You Arrive At Mcdonald S Of The First Student Activity Center And Find That There Are Two Long Lines Line A And Line B 1 (220.71 KiB) Viewed 35 times

You arrive at McDonald's of the First Student Activity Center and find that there are two long lines (Line A and Line B) waiting to be served by the two clerks at the counter. Each clerk is currently serving the student at the head of line (HOL) and you are told by a math guru that the service times of the two clerks for individual students are independent exponential random variables with parameters 11 (Line A) and 12 (Line B) respectively. You need to decide which line to join to order your lunch. . (a) (b) You decide to join the line where its HoL student comes out of service first. What are the probabilities that you choose Line A and Line B respectively? After some careful counting, you find that the length of Line A is about twice of Line B. Hence, you decide to choose Line A only if the first two students in Line A both come out of the service before the first student in Line B does. What is the probability that you choose Line A?