Let's take a random number generator,f, which generated number from let say 1 to 1000, uniformly at random. Now I want to generate 10 numbers uniformly at random from 1 to 100. So if I use f and generates random numbers and take numbers which are in the range 1 to 100, discard otherwise, will those be uniformly at random or not? Why so?
Argument from my side, The probability of coming any number from 1 to 100 in our pick is 1/1000 and it is equally likely for all (I think there is some flaw in this argument but I am not able to find one). So if its true, all the number are equally likely from 1 to 100. That's why they should be random.