A card is randomly selected from a standard deck of 52 cards. Find the probabilities.
P(king or a diamond)
P(spade or a club)
P(4 or a 5)
P(not a heart)
# 2/13
# 3/4
# 1/2
# 4/13



Answer :

Hello! I'm the Brainly AI Helper here to assist you. To find the probabilities of the events mentioned: 1. P(king or a diamond): - Number of kings in a standard deck = 4 (one king of each suit) - Number of diamonds in a standard deck = 13 - Number of cards that are both kings and diamonds = 1 (King of Diamonds) - P(king or a diamond) = (Number of kings + Number of diamonds - Number of both) / Total number of cards - P(king or a diamond) = (4 + 13 - 1) / 52 = 16 / 52 = 4 / 13 2. P(spade or a club): - Number of spades in a standard deck = 13 - Number of clubs in a standard deck = 13 - Number of cards that are both spades and clubs = 0 - P(spade or a club) = (Number of spades + Number of clubs - Number of both) / Total number of cards - P(spade or a club) = (13 + 13 - 0) / 52 = 26 / 52 = 1 / 2 3. P(4 or a 5): - Number of 4s in a standard deck = 4 - Number of 5s in a standard deck = 4 - Number of cards that are both 4s and 5s = 0 - P(4 or a 5) = (Number of 4s + Number of 5s - Number of both) / Total number of cards - P(4 or a 5) = (4 + 4 - 0) / 52 = 8 / 52 = 2 / 13 4. P(not a heart): - Number of hearts in a standard deck = 13 - P(not a heart) = 1 - P(heart) = 1 - (13/52) = 1 - 1/4 = 3/4 Therefore, the probabilities are: 1. P(king or a diamond) = 4/13 2. P(spade or a club) = 1/2 3. P(4 or a 5) = 2/13 4. P(not a heart) = 3/4 I hope this helps you understand the probabilities of the events! If you have any more questions, feel free to ask.