Asked by Shelby
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).
What is the probability that a single card drawn randomly from the deck is a “King” ?
What is the probability that a single card drawn randomly from the deck is not a “King” ?
What is the probability that a single card drawn randomly from the deck is a “Spade” ?
What is the probability that a single card drawn randomly from the deck is not a “Spade” ?
What is the probability that a single card drawn randomly from the deck is a “King” or a “Spade” ?
Use the Addition Rule of Probability: P(A or B)=P(A)+P(B)-P(A and B).
Are the events “King” and “Spade” mutually exclusive? Explain why or why not.
What is the probability that a single card drawn randomly from the deck is a “King” ?
What is the probability that a single card drawn randomly from the deck is not a “King” ?
What is the probability that a single card drawn randomly from the deck is a “Spade” ?
What is the probability that a single card drawn randomly from the deck is not a “Spade” ?
What is the probability that a single card drawn randomly from the deck is a “King” or a “Spade” ?
Use the Addition Rule of Probability: P(A or B)=P(A)+P(B)-P(A and B).
Are the events “King” and “Spade” mutually exclusive? Explain why or why not.
Answers
There are no human answers yet.
Answered by
GPT 3.5
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).
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.
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).
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.
The probability that a single card drawn randomly from the deck is a "King" or a "Spade" can be calculated using the Addition Rule of Probability:
P(King or Spade) = P(King) + P(Spade) - P(King and Spade)
= (4/52) + (13/52) - (1/52)
= 16/52
= 4/13
The events "King" and "Spade" are not mutually exclusive. This is because there is one card in the deck that is both a King and a Spade (the King of Spades). If the events were mutually exclusive, it would mean that there are no cards that satisfy both conditions.
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.
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).
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.
The probability that a single card drawn randomly from the deck is a "King" or a "Spade" can be calculated using the Addition Rule of Probability:
P(King or Spade) = P(King) + P(Spade) - P(King and Spade)
= (4/52) + (13/52) - (1/52)
= 16/52
= 4/13
The events "King" and "Spade" are not mutually exclusive. This is because there is one card in the deck that is both a King and a Spade (the King of Spades). If the events were mutually exclusive, it would mean that there are no cards that satisfy both conditions.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.