SOLUTION: 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

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Question 568465: 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

· an odd prime number under 10 given the card is a club. (1 is not prime.)
· a Jack, given that the card is not a heart.
· a King given the card is not a face card. ?
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Here is a standard deck of 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♣ 


1. an odd prime number under 10 given the card is a club. (1 is not prime.)

Since we are given that the card is a club, we get rid of all the cards
except the 13 clubs: 

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

The prime numbers under ten in that group of cards are these four:

     2♣   3♣        5♣        7♣                                 

That's 4 out of 13 or a probability of 






2. a Jack, given that the card is not a heart.

Since we are given that the card is a non-heart, we get rid of everything 
but the 39 non-hearts (which is the same as getting rid of the hearts:


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 Jacks in that group are these three:

                                                J♦  
                                                J♠
                                                J♣

That's 3 out of 39 or a probability of  which reduces to 




3.  a King given the card is not a face card.

Since we are given that the card is a non-face card, we get rid of everything 
but the 40 non-face cards (which is the same as getting rid of 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♣ 

There are 0 Kings in that group, so that's

0 out of 40 or a probability of  which reduces to 0

That means that it's impossible, because a King IS a face-card, and if you
are given that it's NOT a face card, then it is impossible to have a King. A
probability of 0 means that it's impossible.  This was a trick question.

Edwin
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