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 the drawn card is a King, given that it is a face card, we need to use conditional probability.
Step 1: Determine the total number of face cards in a deck of 52 cards. There are 3 face cards in each suit (Jack, Queen, and King), so a total of 12 face cards in the deck.
Step 2: Determine the number of King cards in the deck. There is only 1 King card in each suit, so a total of 4 King cards in the deck.
Step 3: Calculate the probability. The probability of drawing a King, given that it is a face card, can be calculated as the number of favorable outcomes (drawing a King) divided by the number of total outcomes (drawing a face card). Therefore, the probability is:
Number of King cards / Number of face cards = 4 / 12 = 1/3
So, the probability that the drawn card is a King, given that it is a face card, is 1/3 or approximately 0.3333.
To find the probability that it is a King, given that it is a face card, we need to determine the number of favorable outcomes (King cards) and the total number of possible outcomes (face cards).
There are a total of 12 face cards in a deck (4 Jacks, 4 Queens, and 4 Kings). Out of these 12 face cards, 4 cards are Kings. Therefore, the number of favorable outcomes is 4.
Since there are 12 face cards in total, the total number of possible outcomes is 12.
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes. So, the probability that it is a King, given that it is a face card, is:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 4 / 12 = 1 / 3 = 0.33 (rounded to two decimal places)
Therefore, the probability that a card drawn at random from a deck of 52 cards is a King, given that it is a face card, is approximately 0.33 or 33%.