Ok. Here's a question I just read in a book relating to combinatorics and probability. I'm not able to make head and tail about how I should approach it, so here goes:
You have a device that generates random numbers less than or equal to an integer i. The device has generated x random numbers yet. Compute the probability that the next number it generates, is a repetition.
For example, when i equals 2, and x equal 2, the answer is 50%, as in second move, the device may generate 1 or 2, which was generated previously as well.
So, I tried to think of it as a problem with probability being multiplied in case 1, to those in case 2, and so on, but that doesnt seem to be correct. Similarly, use of sets doesnt yield any merrier results. I'm just utterly confused how I should proceed, the book doesnt even have answers for this odd-numbered question, so stuck between a hard place and a rock. Any pointers to the solution, or entire solutions themselves, would be respected and appreciated.
Thanks in advance!