Final answer:
The probability of drawing a king from a standard deck of 52 cards given that the card is a face card is 1/3. This is because there are 4 kings out of 12 total face cards in the deck. The correct answer is (a) 1/3.
Step-by-step explanation:
The subject of the question is Mathematics, and it involves calculating the probability of drawing a king from an ordinary pack of 52 playing cards, given that the drawn card is a face card.
A standard deck has a total of 12 face cards, which includes jacks, queens, and kings from each suit (clubs, diamonds, hearts, and spades). Since each suit has one king, there are 4 kings in total.
To solve this, we need to calculate the conditional probability of the card being a king, given that it is a face card. The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B), where A is the event that the card is a king, and B is the event that it is a face card.
In our case, P(A|B) = P(King ∩ Face Card) / P(Face Card), which is 4/12 or 1/3. Therefore, the probability is 1/3.