A standard deck contains 52 cards with 4 suits (spades, hearts, diamonds, and clubs) with 13 different denominations (A, K, Q, J, 10, 9, …, 2).
1. What is the probability that a single card drawn randomly from the deck is a “King” ?
The probability that a single card drawn randomly from the deck is a "King" is 4/52 or 1/13. This is because there are 4 Kings in a deck of 52 cards, so the probability is the number of favorable outcomes (4) divided by the total number of possible outcomes (52).
2. What is the probability that a single card drawn randomly from the deck is not a “King” ?
The probability that a single card drawn randomly from the deck is not a "King" is 1 - (4/52) or 48/52. This is because there are 48 cards that are not Kings in a deck of 52 cards, so the probability is 1 minus the probability of drawing a King.
3. What is the probability that a single card drawn randomly from the deck is a “Spade” ?
The probability that a single card drawn randomly from the deck is a "Spade" is 13/52 or 1/4. This is because there are 13 Spades in a deck of 52 cards, so the probability is the number of favorable outcomes (13) divided by the total number of possible outcomes (52).
4. What is the probability that a single card drawn randomly from the deck is not a “Spade” ?
The probability that a single card drawn randomly from the deck is not a "Spade" is 1 - (13/52) or 39/52. This is because there are 39 cards that are not Spades in a deck of 52 cards, so the probability is 1 minus the probability of drawing a Spade.
5. What is the probability that a single card drawn randomly from the deck is a “King” or a “Spade” ?
To find the probability that a single card drawn randomly from the deck is a "King" or a "Spade", we can add the probabilities of drawing a King and drawing a Spade separately and then subtract the probability of drawing a King that is also a Spade.
The probability of drawing a King is 4/52.
The probability of drawing a Spade is 13/52.
The probability of drawing a King that is also a Spade is 1/52 (since there is only 1 King of Spades in the deck).
Therefore, the probability of drawing a "King" or a "Spade" is (4/52) + (13/52) - (1/52) = 16/52 or 4/13.
The probability that a single card drawn randomly from the deck is a "King" or a "Spade" is equal to the sum of the probabilities of drawing a King and drawing a Spade, minus the probability of drawing a card that is both a King and a Spade.
The probability of drawing a King or a Spade can be calculated as follows:
P(King or Spade) = P(King) + P(Spade) - P(King and Spade)
From previous questions, we know that:
P(King) = 4/52
P(Spade) = 13/52
To calculate P(King and Spade), we need to determine how many cards in the deck are both a King and a Spade.
There is only one card in the deck that satisfies this condition, which is the King of Spades. Therefore, P(King and Spade) = 1/52.
Substituting the known values into the formula, we get:
P(King or Spade) = 4/52 + 13/52 - 1/52
P(King or Spade) = 16/52 or 4/13
Therefore, the probability that a single card drawn randomly from the deck is a "King" or a "Spade" is 4/13.
To find the probability that a single card drawn randomly from the deck is a "King" or a "Spade," we need to find the number of outcomes that satisfy this condition and divide it by the total number of possible outcomes.
There are 4 Kings in a deck, and there are 13 Spades in a deck. However, one of the Kings is a spade. So, we can't just add up the number of Kings and Spades to find the total number of favorable outcomes because it would result in double counting.
To avoid double counting, we need to subtract one of the Kings (the one that is also a Spade) from the total count of Kings. Therefore, the number of favorable outcomes is 4 (number of Kings) - 1 (one King that is also a Spade) + 13 (number of Spades) = 16.
The total number of possible outcomes is still 52, as there are 52 cards in a deck.
Therefore, the probability that a single card drawn randomly from the deck is a "King" or a "Spade" is 16/52 or 4/13.