In mathematical terms what is replacement?

Answer 1

Replacement mean we put "it" back before the next step. For example, in drawing cards, replacement means we put the card back before we draw another one. So given an arbitrary collection of objects we want to know what the probability of an event is with replacement. This is equivalent to saying what is the probability of an event when we remove an item from the collections, replace it, mix up the collection, and remove an item again. We can continue doing this infinite number of times.