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 pass through security. What is the probability you’ll make your flight? Given that you miss your flight in the end, how likely is it you got shunted to the slowest security station?

Explanation / Answer

Time taken per passenger by three stations;

i.) 24 / hour

Which means 60 / 24 minutes per passenger = 2.5 minutes per passenger

ii.) 12 / hour

Which means 60 / 12 minutes per passenger = 5 minutes per passenger

iii.) 6 / hour

Which means 60 / 6 minutes per passenger = 10 minutes per passenger

If I get any of first two stations then I will be able to catch the flight because: First one will take total of 5 minutes to check me and the passenger ahead of me and then 5 minutes to reach the gate. Total of 7.5 minuts.

Similarly, it will take exactly 15 minutes to get to the gate if I get second station. Here also I will be able to catch the flight.

But, at third station total time to reach the gate is 25 minutes. This is the only case where I will miss my flight.

P(make the flight) = 2/3

P( slowest station | missed flight) = 1

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