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So we have 4 netflix profiles in a single subscription, say 5 People have access to the account such that 1 of the person is actually piggybacking on other people's profiles.

Assuming that a single show lasts about 2 hours and nobody watches more than 3 shows a day at a maximum. Also everyone sleeps at the same time for 8 hours a day.

What is the probability that all 5 users will log into their account so that the timing of people watching shows clash. how does this probability be affected as more people get access to the account.

Edit : I am pursuing my undergrad in Microbiology. With almost no clue of mathematics and applied mathematics whatsoever. These days I've been inclined to learn a little more about math because of my master's preparation. This question came to me when me and some of my friends pooled in money to get the premium Netflix account.

My thoughts on this problem: initially I thought that 24-8 = 16 so there are just 8 timings for one person to open the account (assuming they watch one show) so if we multipled it (1/8)^4 would be the probability.

Now I know that this answer is wrong because Firstly it only accounts timing in segments. It takes log in at 2 pm and then straight up at 4 pm while completely ignoring 2:01 log in.

Secondly it only takes into account 1 person watching 1 show.

Lastly that is outrageously low probability for the number of times the timings clash for us irl :p

user37060
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  • Welcome to MSE. You'll get a lot more help, and fewer votes to close, if you show that you have made a real effort to solve the problem yourself. What are your thoughts? What have you tried? How far did you get? Where are you stuck? This question is likely to be closed if you don't add more context. Please respond by editing the question body. Many people browsing questions will vote to close without reading the comments. – saulspatz Aug 27 '19 at 17:07
  • I think this question got a really nice background. Can you tell from where did it arrive? Or did you come up with it? If you have no idea or attempts, that's not an issue, but it might be of help if you mention what is your background in math too. – Zacky Aug 27 '19 at 17:09
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    Done. Hope that helps – user37060 Aug 27 '19 at 17:30
  • I think in order to make a reasonable stab at this you need to have some idea of when people are likely to watch TV. For example, it's probably more likely that they'll do it in the evening than during breakfast. If everyone's habits are similar, then that increases the chances of collision. (On the other hand, if one of you is a weirdo who gets all her television-watching out of the way first thing in the morning, maybe that decreases the chances...) – Micah Aug 27 '19 at 18:36
  • Yeah i did figure that but let us say the situation is ideal and anyone could log in at any time – user37060 Aug 27 '19 at 18:37
  • The result of this problem depends heavily on the probability for each person to watch some amount of shows. Is every person's probability equal? Is the chance of watching 0, 1, 2, and 3 shows all 25%, or does it vary? – Gabe Aug 27 '19 at 23:45
  • Yes. Assume people are same in all respects. – user37060 Aug 28 '19 at 21:23

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