You went astray when you declared the expected wait and expected passed.
Draw a number line. Mark it at intervals of 10. Uniformly randomly select a point on that line. The expected average wait and passed (ie forward and reverse directions) are both 5, not 10. The range is 0 to 10.
When you randomize the event occurrences but maintain the interval as an average you change the range maximum and the overall distribution across the range but not the expected average values.
You went astray when you declared the expected wait and expected passed.
Draw a number line. Mark it at intervals of 10. Uniformly randomly select a point on that line. The expected average wait and passed (ie forward and reverse directions) are both 5, not 10. The range is 0 to 10.
When you randomize the event occurrences but maintain the interval as an average you change the range maximum and the overall distribution across the range but not the expected average values.