A deck of cards has 52 cards with 4 suits (Hearts, Diamonds, Spades, and Clubs) and 13 cards in each suit (Ace thru 10, Jack, Queen, and King; the last three are considered face cards). A card is drawn at random from a standard 52-card deck. What is the conditional probability that the card is a face card given that the suit is red is (Hearts and Diamonds are red)?

Answer: [tex]\frac{3}{13}[/tex]Step-by-step explanation:We are given that Total number of cards=52Number of cards in each suit( hearts, spades, clubs, diamond)=13Face cards( king, Queen, Jack)=12Red face cards=6Red suit cards=26We 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]