Question

A card is drawn at random from a pack of 52 cards .what is the probability that the card drawn is neither red nor a black king?

Answer 1

Answer:

Hence, the probability that the card  drawn is neither an ace nor a king 11/13.

Step-by-step explanation:

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)

=13/52+4/52−1/52=16/52

So P(neither heart nor king)=1-P

(heart or king)=1−16/52=36/52=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)=1−8/52=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−(26/52+4/52−2/52)

=1−28/52=24/52=6/13

Answer 2

number of red kings = 2

number of black kings = 2

P (neither red nor black king) = 1 - P(red or black king)

= 1 - (2+2)/52

= 1 - 1/13 = 12/13