Firstly apologies for the vague post title. Apart from probability I don't really know what sub category this question falls within.
If I have a pack of cards and I draw one card from it the chance of pulling a Jack, Queen, King or Ace is 16/52. Then pulling a second is obviously 15/51.
Now if I have a 5 pack of cards the chance of me pulling a Jack, queen, king or ace from any one pack 16/52 * 5. Let's assume pulling one card from each pack is considered a "round".
So for the first round you pull one card from each pack. If you do not pull one of the jack, queen, king or ace card from a pack them you return the card. If however you do pull one of these cards from a pack then you do not return the card to that pack. Instead you play another round which means you pull one more card from each pack. If one of the pack yields one of the cards you are interested in you play another round. The game ends when one round does not give one of those cards.
So in summary 1. Pull one card from all 5 decks 2. Return any cards that you are not interested in. 3. If one or more of the packs gives a card you are interested in do not return it to pack and repeat. 4. Stop when no pack gives interested card.
I want to know how calculate the average number of rounds until the game stops.
Thanks for taking the time to read and for any help you may have.