SOLUTION: 4. A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecti

Question 459356: 4. A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting

�a prime number under 10 given the card is red. (1 is not prime.)
�a King, given that the card is not a heart.
�a nine given the card is a face card.
Show step by step work. Give all solutions exactly in reduced fraction form.

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!




Find the probability of a prime number under 10 given 
the card is red. (1 is not prime.)

Start with a full deck of 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♣ 

Remove all cards except the ones that are given.
We are given that it is red, so we remove all cards
except the red ones.  So we have only these 26:


 
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♦

Now we will select the ones that are prime numbers under 10,
which are the 2's, 3's, 5's, and 7's. I'll enclose them in
brackets:


 
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♦

That's 8 out of 26 or 8/26 which reduces to 4/13

-----------------------------------------------------------

Find the probability of a King, given that the card is not a heart.

Start with a full 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♣ 

Remove all cards except the ones that are given.
We are given that it is not a heart, so we remove all 
the hearts.  So we have only these 39:


  
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♣ 

I'll enclose the kings in brackets:


  
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♣]

That's 3 out of 39 or 3/39 which reduces to 1/13

-----------------------------------------------------------

Find the probability of a nine given the card is a face card.

Start with a full 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♣ 

Remove all cards except the ones that are given.
We are given that it is a face card, so we remove everything but the
face cards.  So we have only these 12:


                               J♥  Q♥  K♥ 
                               J♦  Q♦  K♦
                               J♠  Q♠  K♠  
                               J♣  Q♣  K♣ 

I'll enclose the nines in brackets.  Whoops!  None of them are nines!

That's 0 out of 12 or 0/12 which reduces to 0.

That one was obviously zero because if you're given it's a face card,
then it is impossible that it is a 9, because a 9 is not a face card.

Edwin

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