To find \( P(\text{ace} \mid \text{red}) \), we can use the definition of conditional probability:
\[ P(A \mid B) = \frac{P(A \cap B)}{P(B)} \]
Where:
- \( A \) is the event of choosing an ace.
- \( B \) is the event of choosing a red card.
Step 1: Find \( P(\text{red}) \)
A standard deck of cards has 52 cards in total, 26 of which are red (13 hearts and 13 diamonds).
So,
\[ P(\text{red}) = \frac{26}{52} = \frac{1}{2} \]
Step 2: Find \( P(\text{ace} \cap \text{red}) \)
There are 2 red aces in a deck (the Ace of Hearts and the Ace of Diamonds).
So,
\[ P(\text{ace} \cap \text{red}) = \frac{2}{52} = \frac{1}{26} \]
Step 3: Use the conditional probability formula
Now we can substitute our values into the conditional probability formula:
\[ P(\text{ace} \mid \text{red}) = \frac{P(\text{ace} \cap \text{red})}{P(\text{red})} = \frac{\frac{1}{26}}{\frac{1}{2}} = \frac{1}{26} \times \frac{2}{1} = \frac{2}{26} = \frac{1}{13} \]
Step 4: Convert to decimal and round to the nearest tenth
Now we convert \( \frac{1}{13} \) to a decimal:
\[ \frac{1}{13} \approx 0.0769 \]
Rounded to the nearest tenth, we get:
\[ P(\text{ace} \mid \text{red}) \approx 0.1 \]
Thus, the final answer is:
\[ \boxed{0.1} \]