Deck Card Draw Probability Calculator

Given a deck with cards (1‑500)...
...and drawing total cards into one's hand (0‑99)...
...with there being copies of the desired card in the deck (0‑99)...
...and presuming mulligans, if playing MTG...

...the chances of drawing at least one copy of the desired card is: ???
    AND
...the chances of drawing copies, where X = , is: ???   

NOTE: the second probability ignores the mulligan option