SOLUTION: A card is selected at random from a standard deck of 52 cards. Let A = event the card is a heart B = event the card is a red card Which of the following is (are) true? A: P(A

Question 1032824: A card is selected at random from a standard deck of 52 cards. Let
A = event the card is a heart
B = event the card is a red card
Which of the following is (are) true?
A: P(A or B) = P(A)
B: P(A or B) = P(B)
C: P(A and B) = P(B)
D: P(A and B) = P(A)
Answers:
A) A and D
B) B and C
C) A and C
D) B and D
Found 2 solutions by Boreal, Edwin McCravy:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It is B.
Probability a card is a heart is 1/4 and all hearts are red.
Probability a card is red is 1/2.
A or B is the same as B.
A and B is the same as B.
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
A = event the card is a heart
B = event the card is a red card
Which of the following is (are) true?
A: P(A or B) = P(A)
B: P(A or B) = P(B)
C: P(A and B) = P(B)
D: P(A and B) = P(A)

Here is the universal set of all 52 cards in the deck: cards A♥ 2♥ 3♥ 4♥ 5♥ 6♥ 7♥ 8♥ 9♥ 10♥ J♥ Q♥ K♥ A♦ 2♦ 3♦ 4♦ 5♦ 6♦ 7♦ 8♦ 9♦ 10♦ J♦ Q♦ K♦ A♠ 2♠ 3♠ 4♠ 5♠ 6♠ 7♠ 8♠ 9♠ 10♠ J♠ Q♠ K♠ A♣ 2♣ 3♣ 4♣ 5♣ 6♣ 7♣ 8♣ 9♣ 10♣ J♣ Q♣ K♣ A = event the card is a heart Here is subset A A♥ 2♥ 3♥ 4♥ 5♥ 6♥ 7♥ 8♥ 9♥ 10♥ J♥ Q♥ K♥ There are 13 of them out of the 52 cards, therefore P(A) = 13/52 = 1/4 B = event the card is a red card Here is subset B A♥ 2♥ 3♥ 4♥ 5♥ 6♥ 7♥ 8♥ 9♥ 10♥ J♥ Q♥ K♥ A♦ 2♦ 3♦ 4♦ 5♦ 6♦ 7♦ 8♦ 9♦ 10♦ J♦ Q♦ K♦ There are 26 of them out of the 52 cards, therefore P(B) = 26/52 = 1/2. P(A or B) That's the probability that a card is a heart or a red card, which just means that it is a red card, since hearts are red. Here is the subset A or B: A♥ 2♥ 3♥ 4♥ 5♥ 6♥ 7♥ 8♥ 9♥ 10♥ J♥ Q♥ K♥ A♦ 2♦ 3♦ 4♦ 5♦ 6♦ 7♦ 8♦ 9♦ 10♦ J♦ Q♦ K♦ There are 26 of them out of the 52 cards, therefore P(A or B) = 26/52 = 1/2 P(A or B) is the same as P(B). Therefore B is true. ------------ P(A and B) That's the probability that a card is a heart and a red card, which just means that it is a heart, since hearts are red. Here is subset A and B: A♥ 2♥ 3♥ 4♥ 5♥ 6♥ 7♥ 8♥ 9♥ 10♥ J♥ Q♥ K♥ There are 13 of them out of the 52 cards, therefore P(A and B) = 13/52 = 1/4 P(A and B) is the same as P(A). Therefore D is true. So B and D are true and A and C are false. Edwin

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