Acard is drawn from a standard deck of 52 playing cards. find the probability if the card a) an ace or heart b) an even number or a spade c) a red queen or black face card d) a face card or a heart

A standard deck of 52 playing cards includes 13 of each of the 4 suits : 

clubs , diamonds, hearts and spades. 

Of these, the clubs and spades are black, and the hearts and diamonds are red. 
Each of the 4 suits contains a King, a Queen, and a Jack (The face cards). 

The Sample Space is the set of all possible outcomes in an experiment. Thus, the sample space in our problem is the set containing each of the 52 cards.
The number of this set, is denoted by n(S), and it is equal to 52.

If E is a certain event, then P(E)=n(E)/n(S).

A) E: an ace or heart, what is P(E)?

The event E can occur if any of the 13 hearts is drawn, or if any of the clubs ace , diamonds ace, or spades ace is drawn. 

Thus, n(E)=13+3=16. That is, P(E)=n(E)/n(S)=16/52=0.308

B) E: an even number or a spade. P(E)=?

Event E can occur as follows:

Any spade is drawn, that is 13 cards. Or, any of the cards 2, 4, 6, 8, 10 of one of the clubs , diamonds, or hearts is drawn.

Thus, n(E)=13+5*3=13+15=28.

This means that P(E)=n(E)/n(S)=28/52=0.538

C) E: a red queen or black face card. P(E)=?

There are a total of 2*3=6 black face cards, and 2 red queens. This means that 
                              n(E)=6+2=8.

Thus, P(E)=n(E)/n(S)=8/52=0.154


D) E: a face card or a heart. P(E)=?

There are a total of 13 heart cards, and 3*3=9 non heart, face cards.

Thus, n(E)=13+9=22.

This means that, P(E)=n(E)/n(S)=22/52=0.423

Answers:

A) 0.308

B) 0.538

C) 0.154

D) 0.423