A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is:

(i) either a king or a queen

(ii) neither a king nor a queen

Given,

Total number of outcomes = 52

(i) Let A be the event of getting either a king or a queen, then

∴ The number of favourable outcomes to the event A = 4 (Kings) + 4 (Queens) = 8

∴ P(A) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{8}{52} = \dfrac{2}{13}$

Hence, the probability of getting either a king or a queen is $\dfrac{2}{13}$.

(ii) Let B be the event of getting neither a king nor a queen, then

∴ The number of favourable outcomes to the event B = Total cards - (Kings + Queens) = 44

∴ P(B) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{44}{52} = \dfrac{11}{13}$

Hence, the probability of getting neither a king nor a queen is $\dfrac{11}{13}$.