A single card is drawn from a standard deck of cards. Find the probability if the given information is known about the chosen card. A face card is a jack, queen, or king.
P(face card|king) 4/52
Thank you
Probability of the first one being a king is 4/52
probability of the first one being a face card = 12/52
the probability of the second one being a face card if the first was a king is 11/51
so if you mean probability of choosing a king, then a face card it is
4/52 * 11/51
If you mean conditional probability, meaning
P(Face|King), or probability of a face card given it is a king, then start with the definition of conditional probability:
P(A|B)=P(A∩B)/P(B)
P(Face|King)
=P(Face∩King)/P(king)
=(4/52)/(4/52)
= 1
A king is a face card, that is why
probability of a face card given it's a king equals 1.
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To find the probability of drawing a face card given that the chosen card is a king, you need to determine how many face cards are included among the kings in a standard deck of cards.
In a standard deck, there are 52 cards. Among these, there are 4 kings since there is one king in each suit (hearts, diamonds, clubs, and spades). Since the question asks for the probability of drawing a face card, we need to determine how many face cards are kings.
A face card refers to a jack, queen, or king, and since there are 4 kings in the deck, the number of face cards that are kings is 1.
So, the number of favorable outcomes (drawing a face card that is a king) is 1, and the total number of possible outcomes (drawing any card from the deck) is 52.
Hence, the probability of drawing a face card given that the card is a king is:
P(face card|king) = 1/52
Therefore, the probability is 1/52.