This question is about a Facebook friend problem. If you select a Facebook friend at random, the probability that you have at least as many friends as that person is about 50%. Is that true or false? And why?
So mainly, the question is what is the probability that I would have at least as many friends as the randomly selected friend from FB? Could it be explained simply using probabilities (or Bayes theorem), if so how?
many thanks
Alternative approach without much math.
Assume that there are two people who are going to come in contact on Facebook: Person-1 and Person-2.
Assume that Person-1 has more Facebook friends than Person-2.
Assume that nothing else is known about the two people, other than that one of them is going to reach out to the other, on Facebook.
There are three possibilities:
People with more Facebook friends are significantly more likely than people with fewer Facebook friends to initiate contact.
People with more Facebook friends are significantly less likely than people with fewer Facebook friends to initiate contact.
People with more Facebook friends are neither significantly more likely nor significantly less likely to initiate contact.
Personally, I would consider anything in the ($45$% - $55$%) range to not be significant.
Each of the above assumptions is plausible. Each assumption will lead to a different conclusion on whether the person that you are selecting probably has more Facebook friends than you do, probably has fewer Facebook friends than you do, or neither.
To see this, consider that with you coming into contact with the person that you selected (at random), the contact could have been initiated by the other person, but it wasn't. Similarly, some other Facebook person might randomly contact you.
Personally, my blind speculation is that assumption 1 above is more likely than the other two. It wouldn't surprise me if upwards of $55$% of the time the person who initiates contact has more friends.