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

Count the favourable cards for each description out of the deck's 52 cards, then apply the classical formula to each.

The sample space is $n(S)=52$, every card equally likely (well-shuffled deck).

1. A king: 4 kings in the deck (one per suit), so $n(E)=4$. $P(\text{king}) = \dfrac{4}{52}=\dfrac{1}{13}$.
2. A red card: hearts and diamonds are the red suits, $13+13=26$ red cards, so $n(E)=26$. $P(\text{red}) = \dfrac{26}{52}=\dfrac{1}{2}$.
3. A face card: Jack, Queen, King in each of 4 suits gives $3 \times 4 = 12$ face cards, so $n(E)=12$. $P(\text{face card}) = \dfrac{12}{52}=\dfrac{3}{13}$. …

For part (iii), a common error is including the Ace as a 'face card' (giving $n(E)=16$ instead of 12) — by the standard convention used throughout this chapter, face cards are only Jack …