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

Apply the classical probability formula $P(E)=n(E)/n(S)$ to each event separately, using $n(S)=52$.

Sample space. A standard deck has $52$ cards, so $n(S)=52$.

1. Probability of a king. A deck has $4$ kings (one per suit). $P(\text{king}) = \dfrac{4}{52} = \dfrac{1}{13}$.
2. Probability of a red card. A deck has $26$ red cards (hearts and diamonds, 13 each). $P(\text{red}) = \dfrac{26}{52} = \dfrac{1}{2}$.
3. Probability of a red king. There are exactly $2$ red kings (king of hearts, king of diamonds). $P(\text{red king}) = \dfrac{2}{52} = \dfrac{1}{26}$. …

Counting 'red king' as $4$ (mistakenly counting all kings, forgetting that only the hearts and diamonds kings are red, not the spades and clubs kings) is a common counting slip in card-probability problems — always re-verify a ca …