"The VIP cafeteria door on the Death Star promptly opens at 11:00 am and closes at 1:00 pm (Standard Galactic Time). Nobody is allowed to enter at other times but guests can stay until they finish their meal. To keep their lean physiques, Sith Lords usually spend their allotted 14-minute lunch break in the cafeteria sipping organic kale smoothies. Darth Sidious has a yoga class at 11:00 am, so he never has lunch before noon. Darth Vader must use a straw, so he is allowed an additional 8 minutes to slurp his smoothie. What is the probability that the two of them meet today in the cafeteria?"
For this question, I interpreted it as follows:
The 14 minutes is the average time Siths take to sip their smoothies, but the average for Darth Vader is 22 minutes since he is allowed an extra 8 minutes. Since I have the average, I thought using the exponential probability distribution formula would be the best choice. I also interpreted it as "What is the probability that Darth Vader spends his average 22 minutes between 12:00pm and 1:00pm when the cafe closes", since Sidious can only arrive at the cafe at 12:00pm onwards.
I then used the formula : (1 - e^(-120 ÷ 22)) - (1 - e^(-60 ÷ 22)), but apparently this is wrong.
What am I doing wrong? Is my initial approach of looking at it as exponential decay wrong?