A card is drawn from a standard deck of 52 cards. What is the probability that the card is a heart or a queen?
Practice Questions
1 question
Q1
A card is drawn from a standard deck of 52 cards. What is the probability that the card is a heart or a queen?
1/4
1/13
4/52
17/52
There are 13 hearts and 4 queens, but one of the queens is a heart. Thus, the probability is (13 + 4 - 1)/52 = 16/52 = 4/13.
Questions & Step-by-step Solutions
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Q
Q: A card is drawn from a standard deck of 52 cards. What is the probability that the card is a heart or a queen?
Solution: There are 13 hearts and 4 queens, but one of the queens is a heart. Thus, the probability is (13 + 4 - 1)/52 = 16/52 = 4/13.
Steps: 8
Step 1: Understand that a standard deck has 52 cards.
Step 2: Identify how many hearts are in the deck. There are 13 hearts.
Step 3: Identify how many queens are in the deck. There are 4 queens.
Step 4: Notice that one of the queens is also a heart. This means we have counted it twice.
Step 5: To find the total number of favorable outcomes (hearts or queens), we add the number of hearts and queens, then subtract the one queen that is a heart: 13 (hearts) + 4 (queens) - 1 (queen that is a heart) = 16.
Step 6: The total number of possible outcomes is still 52 (the total number of cards in the deck).
Step 7: Calculate the probability by dividing the number of favorable outcomes by the total number of outcomes: 16/52.
