Got it. I didn’t stop to think it through (System 2 is lazy!), so this is more good luck than good management. Apparently my System 1 is trained to associate “exponential distribution” with “Poisson process” and to replace “most likely” with “mode”. Of course, “exponential distribution” is not quite right; as the answer shows, given the phrasing of the problem statement the relevant distribution is geometric. If the title hadn’t mentioned “Poisson process” I don’t know what would have happened.
Got it. I didn’t stop to think it through (System 2 is lazy!), so this is more good luck than good management. Apparently my System 1 is trained to associate “exponential distribution” with “Poisson process” and to replace “most likely” with “mode”. Of course, “exponential distribution” is not quite right; as the answer shows, given the phrasing of the problem statement the relevant distribution is geometric. If the title hadn’t mentioned “Poisson process” I don’t know what would have happened.