SOLUTION: A single card is drawn from a standard deck of 52 cards. Find the probability the card is: 1. A red four 2. A heart 3. A 4 or a heart. 4. Not a club. 5. A red or a four 6.

Question 591370: A single card is drawn from a standard deck of 52 cards. Find the probability the card is:
1. A red four
2. A heart
3. A 4 or a heart.
4. Not a club.
5. A red or a four
6. A red and a 3
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
A single card is drawn from a standard deck of 52 cards. Find the probability the card is:
1. A red four

There are these 2 red fours 
 
               4♥ 
               4♦

out of these 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♣

That's 2 out of 52, and so we make the fraction  and reduce it to
, and that's the probability.
-----------------------------------------------------------

2. A heart

There are these 13 hearts 

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

out of these 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♣

That's 13 out of 52, and so we make the fraction  and reduce it to
, and that's the probability.
-----------------------------------------------------------

3. A 4 or a heart.

That's any of these 16 cards:


A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥  J♥  Q♥  K♥ 
               4♦
               4♠  
               4♣ 
out of these 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♣ 

That's 16 cards out of 52 cards, and so we make the fraction  and
reduce it to , and that's the probability.
-----------------------------------------------------------

4. Not a club.

That's any of these 39 cards which are not clubs:



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♠  

out of these 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♣ 



That's 39 cards out of 52 cards, and so we make the fraction  and
reduce it to , and that's the probability.
-----------------------------------------------------------


5. A red or a four

That's any of these 28 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♦ 
               4♦
               4♠  

out of these 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♣ 



That's 28 cards out of 52 cards, and so we make the fraction  and
reduce it to , and that's the probability.
-----------------------------------------------------------


6. A red and a 3

[That's just like the 1st one where they said "a red four", they could have
said "a red and a 4".  Or they could have said "a red three" here.  The
words "and a" are redundant.]

That's any of these 2 cards:



          3♥
          3♦

out of these 52:

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♣

Like the 1st one, that's 2 cards out of 52 cards, and so we make the fraction
 and reduce it to , and that's the probability.

Doesn't take a rocket scientist, does it?

Edwin 

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