SOLUTION: A card is selected at random from a standard deck of 52 cards. Let A = event the card is a heart B = event the card is a red card Which of the following is (are) true? A: P(A

Here is the universal set of all 52 cards in the deck:
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♣ 

A = event the card is a heart

Here is subset A


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

There are 13 of them out of the 52 cards, therefore

P(A) = 13/52 = 1/4

B = event the card is a red card

Here is subset B

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♦

There are 26 of them out of the 52 cards, therefore

P(B) = 26/52 = 1/2.

P(A or B)

That's the probability that a card is a heart or a red card,
which just means that it is a red card, since hearts are red.

Here is the subset A or B:

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♦

There are 26 of them out of the 52 cards, therefore

P(A or B) = 26/52 = 1/2  

P(A or B) is the same as P(B).  Therefore B is true.
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P(A and B)

That's the probability that a card is a heart and a red card,
which just means that it is a heart, since hearts are red.

Here is subset A and B:


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

There are 13 of them out of the 52 cards, therefore

P(A and B) = 13/52 = 1/4  

P(A and B) is the same as P(A).  Therefore D is true.

So B and D are true and A and C are false.

Edwin