A card is randomly selected from a standard deck of playing cards. Find the probability that it is a face card, given that a black card is drawn.

 The final answer, as a fraction, is 8/13    

Step-by-step explanation:

A = number of black cards

B = number of picture cards (or face cards)

C = number of black picture cards  

There are 26 black cards (spades and clubs), so A = 26.  

There are 3 picture cards (Jack, Queen, King) in each suit. There are 4 suits (clubs, hearts, spades, diamonds). So there are 3*4 = 12 picture cards. This means B = 12  

There are 2 suits which are black (spades and clubs) with 3 face cards per suit, so 2*3 = 6 cards which are both black cards and face cards. So C = 6  

The number of cards that are either black cards or a face card, or both, is...  

D = A+B-C

D = 26+12-6

 D = 32  

So there are 32 cards that are either black cards or a face card, or both  This is out of 52 cards total, so  

probability of selecting a black card or a picture card = D/52  

probability of selecting a black card or a picture card = 32/52  

probability of selecting a black card or a picture card = 8/13  

what is the original number? you forgot to add it.