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I can solve basic problems of chance of dependent and independent events. The following portion of question is an excerpt of my algorithm which i am developing for an autonomous contention based queuing system to mitigate collisions in a communication system. I want to calculate the following in terms of probability. This will help me to see how the algorithm performs for varying number of 'n' in the following question.

A group of n people generate a 64-bit number e.g., (0 1 1 0 1 0 1 0 1 0 0 1 1 . . . ) independently of each other. The 64-bit number is randomly generated by every individual and it is assumed to have an avalanche effect. It means that the binary values of two persons are significantly different. Now the decimal equivalent of the binary 64-bit value is translated by every person to a number x in the range [1, 50] using the formula

x=[(old_value - old_min)/(old_max - old_min)]*(new_max - new_min) + new_min

Then what is the probability that the same x is calculated by least two people.

Divyessh
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tina saleem
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    I think the easiest way would be to run simulations. If you want to calculate anything you'll have to be precise about exactly how the 64 bit numbers are generated and in particular what 'avalanche effect' means. – dmuir Oct 06 '20 at 08:18
  • no information is provided as to what old_value, old_min, etc. are or how their values are calculated. Why should that formula yield a value in [1,50]? – President James K. Polk Oct 06 '20 at 22:53

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