a card is darawn from apack of 52 cards. find

1)neither a heart nor aking

2) naither a ace nor a king

3) neither a red nor a queen.

Total number of playing cards = 52
So the number of ways of drawing 1 card out of 52 cards =52
So n(S) = 52
(1) Drawn card is neither a heart nor a king
So probability of this can be obtained by (1- probability that the drawn card is heart or a king)
So total number of hearts = 13
Total number of kings = 4
and 1 card is both heart and king 
So P(heart or king) =P(heart)+P(king)-P(heart and king)
or $P(heart or king)=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}=\frac{16}{52}$
So P(neither heart nor king)=1-P(heart or king)=$1-\frac{16}{52}=\frac{36}{52}=\frac{9}{13}$
(2)  Drawn card is neither an ace nor a king
There are 4 aces and 4 kings  ,  so total 8 cards
So P(neither ace nor king)=1-P(ace or king)=$1-\frac{8}{52}=\frac{11}{13}$
(3)Drawn card is neither a red nor a queen 
Number of red cards = 26
Number of queens =4
and  number of cards  which is queen and red =2
So P(drawn card is neither red nor queen)= 1-[P( red card)+P( queen)-P( red and queen)]
$so P(drawn card is neither red nor queen)=1-(\frac{26}{52}+\frac{4}{52}-\frac{2}{52})=1-\frac{28}{52}=\frac{24}{52}=\frac{6}{13}$