Math Problem Statement
In a standard deck of cards, what is the probability of drawing a diamond OR a face card (answer choices are in the form of a percentage, rounded to the nearest whole number)?
Solution
In a standard deck of 52 cards, let's break down the problem of finding the probability of drawing a diamond OR a face card.
-
Number of Diamonds:
There are 13 diamonds in a deck (one for each rank: 2, 3, ..., 10, J, Q, K, A). -
Number of Face Cards:
There are 12 face cards in a deck (4 Jacks, 4 Queens, and 4 Kings, with one of each in each suit: hearts, diamonds, clubs, and spades). -
Overlapping Cards (Diamonds that are also Face Cards):
There are 3 face cards in the diamond suit (the Jack, Queen, and King of diamonds).
We will use the inclusion-exclusion principle to avoid double-counting these overlapping cards:
Substituting values:
Now, calculate this:
Converting this to a percentage:
Rounding to the nearest whole number gives:
Would you like more details or have any other questions?
Here are 5 related questions:
- What is the probability of drawing a spade or an Ace from a deck of cards?
- How many face cards are there in a deck, excluding diamonds?
- What is the probability of drawing a red card (hearts or diamonds) from the deck?
- What is the probability of drawing a card that is neither a face card nor a diamond?
- What is the probability of drawing a card that is a number card (2-10) or a spade?
Tip: For probability involving multiple events, use the inclusion-exclusion principle to avoid double-counting overlapping outcomes.
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Math Problem Analysis
Mathematical Concepts
Probability
Set Theory
Inclusion-Exclusion Principle
Formulas
P(A or B) = P(A) + P(B) - P(A and B)
Theorems
Inclusion-Exclusion Principle
Suitable Grade Level
Grades 9-12
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