A card is drawn at random from a deck of 52 cards. What is
a probability that it is a King, given that it is a face card (J, Q, K)?
To find the probability that a card is a King, given that it is a face card, we need to use the concept of conditional probability.
Step 1: Determine the number of favorable outcomes.
The deck contains 52 cards, and there are 4 Kings in a deck, so there are 4 favorable outcomes.
Step 2: Determine the number of total outcomes.
Since we know that the card is a face card (J, Q, or K), there are 3 face cards of each suit, resulting in a total of 12 face cards in the deck.
Step 3: Calculate the probability using the formula:
Probability = Number of favorable outcomes / Number of total outcomes
Probability = 4 / 12
Simplifying this fraction, we get:
Probability = 1 / 3
Therefore, the probability that the card drawn is a King, given that it is a face card, is 1/3 or approximately 0.333.