The chance that the top card in the deck is a face card given that the eighth card from the top is a seven is?

Question

The chance that the top card in the deck is a face card given that the eighth card from the top is a seven is?

Answer 1

If the eighth card from the top is a seven, then there are 51 possible cards the top one could be (any of the 48 non-sevens, plus the three other sevens).  There are twelve face cards in the deck*, so the odds would be 12 in 51.

* This assumes you are using the term "face card" strictly to mean a Jack, Queen, or King.  Some people use the term more loosely to include Tens and/or Aces.  If so, the odds increase to either 16 in 51 (if you include Tens or Aces but not both) or 20 in 51 (if you include both Tens and Aces).