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)?

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.

1. **Number of Diamonds**:  
   There are 13 diamonds in a deck (one for each rank: 2, 3, ..., 10, J, Q, K, A).

2. **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).

3. **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:

\[
\text{P(Diamond or Face Card)} = \frac{\text{Number of Diamonds} + \text{Number of Face Cards} - \text{Number of Overlapping Face Diamonds}}{\text{Total Number of Cards}}
\]

Substituting values:

\[
\text{P(Diamond or Face Card)} = \frac{13 + 12 - 3}{52} = \frac{22}{52}
\]

Now, calculate this:

\[
\frac{22}{52} \approx 0.4231
\]

Converting this to a percentage:

\[
0.4231 \times 100 = 42.31\%
\]

Rounding to the nearest whole number gives:

\[
\boxed{42\%}
\]

Would you like more details or have any other questions?

Here are 5 related questions:
1. What is the probability of drawing a spade or an Ace from a deck of cards?
2. How many face cards are there in a deck, excluding diamonds?
3. What is the probability of drawing a red card (hearts or diamonds) from the deck?
4. What is the probability of drawing a card that is neither a face card nor a diamond?
5. 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.

Discover the probability of drawing a diamond or a face card from a standard deck of 52 cards. This detailed guide covers key concepts such as the inclusion-exclusion principle and the formula to avoid double-counting overlapping outcomes. Suitable for high school students (Grades 9-12).

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