A card is drawn at random from a well-shuffled deck of 52 playing cards. Find the probability that it is (a) a king, (b) a red card, and (c) a face card.

Step 1: Identify Total Outcomes

In a standard deck of playing cards, there are 52 cards in total. This represents the total number of possible outcomes when drawing a single card.

Step 2: Calculate Probability of Drawing a King

There are 4 Kings in a deck of 52 cards (King of Spades, King of Clubs, King of Hearts, King of Diamonds). The probability of drawing a King is the ratio of the number of Kings to the total number of cards.

Step 3: Calculate Probability of Drawing a Red Card

A standard deck has two red suits: Hearts and Diamonds. Each suit has 13 cards, so there are $13 + 13 = 26$ red cards. The probability of drawing a red card is the ratio of the number of red cards to the total number of cards.

Step 4: Calculate Probability of Drawing a Face Card

Face cards include Kings, Queens, and Jacks. Since there are 4 suits, and each suit has 3 face cards, the total number of face cards is $3 \times 4 = 12$. The probability of drawing a face card is the ratio of the number of face cards to the total number of cards.

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