You are waiting in the security line at the San Diego International Airport. Whe

Question

You are waiting in the security line at the San Diego International Airport. When you get to the TSA agent, she directs you to one of three security stations at random, each of which just started serving a traveler in front of you. The stations check through passengers at different average rates: 24/hour, 12/hour, and 6/hour. Your flight will close in 15 minutes, and it takes 5 minutes to get to the gate once you begin the security process (you have TSA PRE, so it takes very little time once it’s finally your turn). (a) What is the probability you’ll make your flight? (b) Given that you miss your flight in the end, how likely is it you got shunted to the slowest security station?

Explanation / Answer

Solution:

Probability of passing through each gate=1/3

(a) Probability of getting flight=1/3(1/6+1/3+2/3)=7/18

(b) Probability that missing a flight=10/15

Security Station 1 Security Station 2 Security Station 3 24/hr 12/hr 6/hr 2.5minute/passing 5minute/passing 10minute/passing

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