I've taken the day off to wait for a parcel at home and (because I'm a physics student and therefore have no ability to actually(adsbygoogle = window.adsbygoogle || []).push({}); enjoymy day off) I got thinking about this as a problem.

Suppose the delivery company is perfect, i.e. if they say they're going to deliver between 09:00 and 18:00 then they certainly will. If I need to go out to do something which takes 1 hour to do in the delivery time slot, when should I go?

My first guess would be at 09:00. At 09:00 there is a 1/540 chance it will come during any given minute. If it hasn't come at 09:59 then it must come between 10:00 and 18:00 and so the probability increases to 1/480 per minute, until the last hour is 1/60 per minute, meaning that if it hasn't come by 16:59 I have to leave at 17:00 and will surely miss my parcel. (1/60 per minute * 60 minutes).

But. I think there's a problem with that. Suppose we go back to the beginning. At 09:00 there is a 1/540 probability the parcel will come in any given minute. So at 4:59 there have been 480 minutes and there will be 60 minutes left. So the probability it will come before then is 8 times larger than the probability it will come in the last 60 minutes. Thinking this way would require me to plan to go out in the last hour.

So my two answers are, the first hour or the last hour.

Does anyone have any thoughts on this? Or would like to point out where my faulty logic is?

Thank you.

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# The Parcel Problem

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