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.