A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces
(aces are not face cards find the probability of selecting. an eight given the card is not a face card. a club given the card is red. A king,given the card is red.
You need to punctuate and capitalize your questions better. You are asking three separate questions.
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Find the probability of selecting:
(a) An eight given the card is not a face card.
The answer is 4/40 = 1/10
(b) A club given the card is red.
The answer is zero. There are no red clubs.
(c) A king, given the card is red.
The answer is 2/26 = 1/13
The subject is probability, not geometry
To find the probability of selecting a specific card, we need to determine the number of favorable outcomes (cards that meet the given condition) and the number of total possible outcomes (total number of cards in the deck).
1) Probability of selecting an eight given the card is not a face card:
Since each suit (clubs, diamonds, hearts, and spades) contains one eight, there are four eights in total. Face cards consist of twelve cards in each suit (king, queen, and jack). So the number of non-face cards is 52 - 12 = 40. Therefore, the probability of selecting an eight given the card is not a face card is 4/40, which simplifies to 1/10.
2) Probability of selecting a club given the card is red:
There are two red suits (diamonds and hearts) in a standard deck, each containing 13 cards. Clubs are always black, so there are no clubs among the red cards. Therefore, the probability of selecting a club given the card is red is 0.
3) Probability of selecting a king given the card is red:
Again, there are two red suits (diamonds and hearts) in a standard deck, each containing 13 cards. Among these 26 red cards, there are two kings (one in each red suit). Therefore, the probability of selecting a king given the card is red is 2/26, which simplifies to 1/13.
Remember, when calculating probabilities, divide the number of favorable outcomes by the number of total outcomes.