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.
