Question

A card is drawn at random from a well-shuffled deck of $52$ playing cards. Find the probability that the card drawn is (i) a card of spades or an ace, (ii) a black king, (iii) neither a jack nor a king, (iv) either a king or a queen.

Answer 1

i)There are 13 spades including its ace and 3 other aces are there of other suits so the probability of getting spade or ace$=\frac{(13+3)}{52}=\frac{16}{52}=\frac{4}{13}$

ii)There are two black king so probability$=\frac{2}{52}=\frac{1}{26}$

iii) There are 4 jack and 4 king so cards which are neither jack nor king$=52-8=44$

Probability$=\frac{44}{52}=\frac{11}{13}$

iv) There are 4 king and 4 queen so probability$=\frac{8}{52}=\frac{2}{13}$