SOLUTION: We are drawing a single card from a standard​ 52-card deck. Find the following probability. P( three | non face card)

The probability of drawing a three, given that it is a non face card.

Here is the COMPLETE sample space of all 52 cards:


 
A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥  J♥  Q♥  K♥ 
A♦   2♦   3♦   4♦   5♦   6♦   7♦   8♦  9♦  10♦  J♦  Q♦  K♦
A♠   2♠   3♠   4♠   5♠   6♠   7♠   8♠  9♠  10♠  J♠  Q♠  K♠  
A♣   2♣   3♣   4♣   5♣   6♣   7♣   8♣  9♣  10♣  J♣  Q♣  K♣ 

Below is the reduced sample space found by taking away everything 
from the complete sample space that is not given.  Here we are given 
that it is a non-face card, so we take away all 12 face cards, 
leaving the 40 non-face cards.


 
A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥   
A♦   2♦   3♦   4♦   5♦   6♦   7♦   8♦  9♦  10♦
A♠   2♠   3♠   4♠   5♠   6♠   7♠   8♠  9♠  10♠  
A♣   2♣   3♣   4♣   5♣   6♣   7♣   8♣  9♣  10♣ 

Now from that reduced sample space, only 4 of them are threes.  So
the probability is "4 out of 40, or 4/40 which reduces to 1/10.

Edwin