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)=1352+452-152=1652
So P(neither heart nor king)=1-P(heart or king)=1-1652=3652=913
(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)=1-852=1113
(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-(2652+452-252)=1-2852=2452=613
 

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