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.

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 $P(heartorking)=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}=\frac{16}{52}$

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)]

$soP(drawncardisneitherrednorqueen)=1-(\frac{26}{52}+\frac{4}{52}-\frac{2}{52})=1-\frac{28}{52}=\frac{24}{52}=\frac{6}{13}$

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