newbie question

I took a stats class about 20 years ago so apologizes up front if the answer here should be obvious.

Scenario is an online forum where there is suspicion one person is using 3 different user profiles. Checking the profiles in question shows all three are set to invisible mode. This user-controlled option is a binary value, either visible or invisible. Clicking on 50 other profiles in the forum reveals 4 were set to invisible, so this is not a commonly used setting. User admits to having a second profile but has not revealed which profile is the second one. Is there a way to get the probability of any three selected profiles all being set to invisible or is there missing information needed to calculate this? Thanks.


Less is more. Stay pure. Stay poor.
Is this a real-life problem or learning question? Are there any other pertinent data available? Can you check IP address?

Do you know how many profiles there are and how many are set to invisible beyond your sample of 50. Was the sample of 50 done at random or is it a convenience sample?
Real world. Forum has over 400,000 users across at least 20 subforums so I guess sampling would be complicated. To get the sample of 50 I started at the most recent thread in the subforum of interest and went down the next 49 threads looking at the profile of the last person to post in the each thread - that's where I got the 4 out of 50 users having hidden profiles. I'm not trying to identify the person's real identity so I don't care what their IP address is. The user laid down the gauntlet to the rest of the community by admitting they are using 2 profiles but not divulging their primary profile name. The point is the user thinks they are being slick and some humble pie in the form of a convincing probability regarding the chances of two or three random profiles being in hidden mode would be amusing. Others have already speculated two of the profiles are connected but no one has noticed the hidden profile aspect.


TS Contributor
Is there a reason you can't just check the IP addresses? I am a forum moderator in a different discussion forum using an older version of vbulletin. You can look up the IP address of the known userid, then check for all userid's that have that IP address.

I've never seen your particular scenario. Usually, the multiple userid scenario is either done to get around a banned userid, or to exhibit multiple personalities. That is, a public persona, and an alternate persona that will say things that the public persona would not like to be attributed back to them.
I would say that there is missing information because of the fact that so many variables would go into whether or not a specific profile would be set to invisible. I would say that you could easily calculate exactly what the statistics are for what the probability is if any three profiles being set to invisible are. There are methods, however, of coming to a logical conclusion of whether or not one particular individual created three separate profiles. There will always be constants no matter how many profiles the person creates. No matter what one does, there are always finger prints because everything they create and do comes from their own unique perspective of the world. It would take some time and evaluation, but you could eventually find common factors that the same person wouldn't be able to avoid among the three profiles they created.