SOLUTION: If a single card is drawn from an ordinary deck of card, what is the probability of drawing either a heart or a picture card (king, queen or jack)

There are two methods to do this problem:

Method 1:

Here are all 52 cards in a deck:


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♣  

The ones which fit that description as either a heart or a picture card 
(king, queen or jack), are these 22 cards:

A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥  J♥  Q♥  K♥ 
                                                J♦  Q♦  K♦
                                                J♠  Q♠  K♠  
                                                J♣  Q♣  K♣
 
So the answer is 22 out of 52 or  which reduces to .

Method 2:

By formula: P(A or B) = P(A) + P(B) - P(A and B)

P(♥ or FACE) = P(♥) + P(FACE) - P(♥ and FACE)
             =    +      -    
             =  
             =  
             =     

Edwin