# Using Poisson distribution to estimate if a printer is available? (I have the solution but don't understand it) [SOLVED]

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.

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I don't think the problem is right (though perhaps it's a reasonable approximation). It implicitly allows other jobs to overlap! –  Charles Oct 3 '10 at 23:01
The problem needs additional assumptions. For example, suppose jobs are submitted in bursts of 11 on the hour: then the probability is 10/11 that a job will be queued while another is printing. –  whuber Oct 4 '10 at 14:13