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  

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1