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 drawn at random from a deck of 52 cards is a King, given that it is a face card (J, Q, K), we need to determine the number of favorable outcomes and the total number of possible outcomes.
1. Determine the number of favorable outcomes:
Since we know the card is a face card (J, Q, K), there are 3 possible Kings in a deck.
2. Determine the total number of possible outcomes:
In a deck of 52 cards, there are 12 face cards (J, Q, K). So, the total number of possible outcomes is 12.
3. Calculate the probability:
The probability is the number of favorable outcomes divided by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
In this case, there are 3 favorable outcomes (Kings) and 12 total possible outcomes (face cards).
Probability = 3/12 = 0.25
So, the probability that a card drawn at random from a deck of 52 cards is a King, given that it is a face card (J, Q, K), is 0.25 or 25%.