My friend is taking a course on probabilities and come across a problem that has a solution we both have trouble understanding:
A single printer prints, on average, 22 jobs an hour. Let's use a simplification where no job takes more than 2 minutes to complete. Using these assumptions, calculate the upper limit for the probability that, when a job arrives to the printer, the printer is processing another job.
The solution was to use the Poisson distribution: 1 - ((22/30)^0)*e^(-22/30)/1! = 1 - e^(-22/30) = ~0.52
I'm having trouble believing this: wouldn't simply 22/30 make more sense? Even though I can see how enqueueing the printing jobs is Poisson distributed, how come that goes for the waiting times, too? Or have they messed up with the solutions?
Edit: after sending feedback the assistant said the problem was, indeed, ambiguous. Thanks for the help.