Answer: [tex]\dfrac{2}{3}[/tex]
Step-by-step explanation:
Total number of cards in a deck = 52
Number of face cards = 12 ( 4 King + 8 others)
The probability that a card is face card P(Face card)= [tex]\dfrac{\text{Number of face cards }}{\text{Total cards}}[/tex]
[tex]\\\\=\dfrac{12}{52}=\dfrac{3}{13}[/tex]
Number of cards are not king = 8
The probability that a card is face card are not King :
P( Face card and not king )= [tex]\dfrac{\text{Number of face cards are not King}}{\text{Total cards}}[/tex]
[tex]\\\\=\dfrac{8}{52}=\dfrac{2}{13}[/tex]
Using conditional probability formula ,
[tex]\text{P(Not king}|\text{ Face card})=\dfrac{\text{P( Face card and not king )}}{\text{ P(Face card)}}[/tex]
[tex]=\dfrac{\dfrac{2}{13}}{\dfrac{3}{13}}=\dfrac{2}{3}[/tex]
Hence, the probability that it is not a king given that it is a face card [tex]=\dfrac{2}{3}[/tex]
