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

**Probability the card drawn is a face card.**
 

**Probability the card drawn is not a face card.**
 

**Odds in favor of drawing a face card.**
 

**Odds against drawing a face card.**

Let's address each part of the problem step by step.

### 1. **Probability the card drawn is a face card.**

A standard 52-card deck contains 12 face cards (Jack, Queen, King from each suit: Hearts, Diamonds, Clubs, and Spades).

The probability \( P(\text{face card}) \) is calculated as:
\[
P(\text{face card}) = \frac{\text{Number of face cards}}{\text{Total number of cards}} = \frac{12}{52} = \frac{3}{13}
\]

### 2. **Probability the card drawn is not a face card.**

The number of non-face cards is \( 52 - 12 = 40 \).

The probability \( P(\text{not a face card}) \) is:
\[
P(\text{not a face card}) = \frac{\text{Number of non-face cards}}{\text{Total number of cards}} = \frac{40}{52} = \frac{10}{13}
\]

### 3. **Odds in favor of drawing a face card.**

The odds in favor of an event are the ratio of the probability of the event happening to the probability of it not happening.

So, the odds in favor of drawing a face card are:
\[
\text{Odds in favor} = \frac{\text{Number of face cards}}{\text{Number of non-face cards}} = \frac{12}{40} = \frac{3}{10}
\]

### 4. **Odds against drawing a face card.**

The odds against an event are the inverse of the odds in favor. Thus, the odds against drawing a face card are:
\[
\text{Odds against} = \frac{\text{Number of non-face cards}}{\text{Number of face cards}} = \frac{40}{12} = \frac{10}{3}
\]

### Final Results:
1. Probability the card drawn is a face card: \( \frac{3}{13} \)
2. Probability the card drawn is not a face card: \( \frac{10}{13} \)
3. Odds in favor of drawing a face card: \( \frac{3}{10} \)
4. Odds against drawing a face card: \( \frac{10}{3} \)

Would you like more details on any step or further clarifications?

Here are five related questions to expand your understanding:
1. What is the probability of drawing an Ace from a standard deck?
2. What are the odds in favor of drawing a red card?
3. What is the probability of drawing a King from the deck?
4. What are the odds against drawing a numbered card (2 through 10)?
5. What is the probability of drawing a black card?

**Tip:** Remember, odds are expressed as a ratio comparing two quantities, while probability is a ratio of favorable outcomes to total outcomes.

A card is drawn randomly from a standard 52-card deck. Find the following: Probability the card drawn is a face card. Probability the card drawn is not a face card. Odds in favor of drawing a face card. Odds against drawing a face card.

Explore the probability and odds of drawing a face card from a standard 52-card deck. Learn how to calculate the probability of drawing a face card (3/13) and not drawing one (10/13), along with the odds in favor (3/10) and against (10/3) drawing a face card. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation