A card is drawn from a well shuffled deck of 52 playing . . .

Question : A card is drawn from a well shuffled deck of 52 playing cards. A card is drawn at random find the probability that the card drawn is a 

i) face card

ii) a red or a king card (either a red or a king card)

iii) red and a king card

iv) neither a red card nor a king card

v) either an ace or a face card

vi) green card

Doubt by Lakshay and Yashika

Solution : 

Total No. of playing cards in a deck = 52

P(E) =
[Number of favorable outcomes]/[Total number of possible outcomes]

i) There are 12 face (3 cards from each suit) cards in a deck.

P(Face Cards)
= 12/52
= 3/13

ii) Total No. of Red Cards = 26

Total No. of King Cards = 4

No. of cards which are both Red and King = 2

Total No. of cards which are either red or king = 26+4-2 = 28

P(Either Red or a King Card)
= 28/52
= 7/13

iii) Total No. of cards which are both Red as well as king = 2

P(Red and a King Card)
= 2/52
= 1/26

iv) We know, 
P(not E) = 1-P(E)
P(Neither a Red Card nor a King Card) 
= 1- (Either a Red Card or a King Card)

= 1-[7/13]
=(13-7)/13
= 6/13

v) Total No. of Ace Cards = 4

Total No. of Face Cards = 12

Total No. of cards which are both Ace and Face cards = 0

Total No. of cards which are either an ace or a face card = 4+12 = 16

P(either an ace or a face card) = 16/52

=4/13

v) Total No. of Green Cards = 0
P(green cards)
= 0/52
= 0