Question

While shuffling a pack of 52 cards, one card was accidently dropped. Find the probability that the dropped card

1. is not a face card. 
2. is a black king. 

Answer 1

Given: Total cards, \[ n(S) = 52 \]

(i) Dropped card is not a face card:

There are 12 face cards (Kings, Queens, Jacks). 

Number of non-face cards = `(52 - 12 = 40)`

\[ P(\text{not a face card}) = \dfrac{40}{52} = \dfrac{10}{13} \]

(ii) Dropped card is a black king:

There are 2 black kings (King of Spades and King of Clubs). 

\[ P(\text{black king}) = \dfrac{2}{52} = \dfrac{1}{26} \]