A card is drawn randomly from a standard 52-card deck. Find the following:
Write all answers as simplified fractions (not mixed numbers).
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
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UpStudy AI · Accepted Answer

**Step 1: Find the probability of drawing a face card.**

A face card is a Jack, Queen, or King. There are 3 face cards per suit and 4 suits, so there are  
$$
3 \times 4 = 12 \text{ face cards}
$$
in a standard 52-card deck. Thus, the probability is  
$$
\frac{12}{52} = \frac{3}{13}.
$$

**Step 2: Find the probability of drawing a card that is not a face card.**

There are  
$$
52 - 12 = 40 \text{ non-face cards}.
$$
Thus, the probability is  
$$
\frac{40}{52} = \frac{10}{13}.
$$

**Step 3: Determine the odds in favor of drawing a face card.**

Odds in favor are given by the ratio of the number of successful outcomes (face cards) to the number of unsuccessful outcomes (non-face cards):  
$$
\text{Odds in favor} = 12 : 40.
$$
Simplify the ratio by dividing both numbers by 4:  
$$
12 : 40 = 3 : 10.
$$

**Step 4: Determine the odds against drawing a face card.**

Odds against are the inverse ratio (non-face cards to face cards):  
$$
\text{Odds against} = 40 : 12.
$$
Simplify the ratio by dividing both numbers by 4:  
$$
40 : 12 = 10 : 3.
$$

**Final Answers:**
- Probability the card drawn is a face card: $$ \frac{3}{13} $$
- Probability the card drawn is not a face card: $$ \frac{10}{13} $$
- Odds in favor of drawing a face card: $$ 3:10 $$
- Odds against drawing a face card: $$ 10:3 $$
- Probability of drawing a face card: $$ \frac{3}{13} $$ - Probability of not drawing a face card: $$ \frac{10}{13} $$ - Odds in favor of drawing a face card: $$ 3:10 $$ - Odds against drawing a face card: $$ 10:3 $$

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