Answer:
[tex]\frac{3}{13}[/tex]
Step-by-step explanation:
We are given that
Total number of cards=52
Number of cards in each suit( hearts, spades, clubs, diamond)=13
Face cards( king, Queen, Jack)=12
Red face cards=6
Red suit cards=26
We have to find the conditional probability that the card is a face card given that the suit is red .
Conditional probability: [tex] P(A/B)=\frac{P(A\cap B)}{P(B)}[/tex]
P(red suit card)=[tex]\frac{26}{52}[/tex]
P(Red suit face card)=[tex]\frac{6}{52}[/tex]
P(face card/red suit card)=[tex]\frac{\frac{6}{52}}{\frac{26}{52}}[/tex]
P(face card/red suit card)=[tex]\frac{6}{26}=\frac{3}{13}[/tex]
Answer: [tex]\frac{3}{13}[/tex]
