A card is drawn from a standard deck of 52 cards. What is the probability that i

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Question: A card is drawn from a standard deck of 52 cards. What is the probability that it is a heart or a queen?

Options:

Correct Answer: 17/52

Solution:

There are 13 hearts and 4 queens, but one queen is a heart. So, the probability is (13 + 4 - 1)/52 = 16/52 = 4/13.

A card is drawn from a standard deck of 52 cards. What is the probability that it is a heart or a queen?

A card is drawn from a standard deck of 52 cards. What is the probability that it is a heart or a queen?

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 (the queen of hearts).
Step 5: To find the total number of favorable outcomes (hearts or queens), add the number of hearts (13) and the number of queens (4).
Step 6: Since one queen is already counted as a heart, subtract 1 from the total to avoid double counting. So, the total is 13 + 4 - 1 = 16.
Step 7: The probability is the number of favorable outcomes (16) divided by the total number of cards (52).
Step 8: Calculate the probability: 16/52.
Step 9: Simplify the fraction 16/52 to 4/13.

Probability of Combined Events – This question tests the understanding of calculating probabilities for combined events, specifically using the principle of inclusion-exclusion.
Counting Principles – It assesses the ability to count distinct outcomes correctly, particularly when dealing with overlapping categories (hearts and queens).