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.
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.
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