**A card is drawn randomly from a standard 52-card deck. Find the following:**
*Write all answers as simplified fractions.*
**Odds against drawing a face card.**

A standard 52-card deck has 12 face cards: 4 Jacks, 4 Queens, and 4 Kings. The total number of cards is 52.

### Step 1: Calculate the probability of drawing a face card
The probability of drawing a face card is:

\[
P(\text{Face card}) = \frac{12}{52} = \frac{3}{13}
\]

### Step 2: Calculate the probability of **not** drawing a face card
The probability of **not** drawing a face card is:

\[
P(\text{Not a face card}) = 1 - P(\text{Face card}) = 1 - \frac{3}{13} = \frac{10}{13}
\]

### Step 3: Calculate the odds against drawing a face card
The **odds against** drawing a face card is the ratio of the probability of **not** drawing a face card to the probability of drawing a face card:

\[
\text{Odds against drawing a face card} = \frac{P(\text{Not a face card})}{P(\text{Face card})} = \frac{\frac{10}{13}}{\frac{3}{13}} = \frac{10}{3}
\]

So, the odds against drawing a face card are \( \boxed{\frac{10}{3}} \).

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Do you want more details or have any questions?

Here are 5 related questions for further practice:
1. What are the odds against drawing a King specifically?
2. What is the probability of drawing a red card?
3. What are the odds in favor of drawing a face card?
4. What is the probability of drawing a non-face card?
5. How many total black face cards are in the deck?

**Tip:** When calculating odds, always express them as a ratio between two probabilities—favoring an outcome vs. against that outcome.

A card is drawn randomly from a standard 52-card deck. Find the following: Odds against drawing a face card.

Explore the calculation of the odds against drawing a face card from a standard 52-card deck. This problem includes key probability concepts and the odds calculation formula. Suitable for students in Grades 7-9.

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